Angles

Problem 701

Find $m \angle T U 1$ if $m \angle T U 1=2x+43$ , $m \angle I U V=135^\circ$ , and $m \angle T U V=x+178$ .

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Problem 702

If $\angle A$ complements $\angle B$ and $m \angle A=36^{\circ}$ , find $m \angle B$ .

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Problem 703

Find the measure of angle C if it supplements angle D, where $m \angle D = 117^{\circ}$ .

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Problem 704

Sara was asked to drawn a parallelogram. She drew the figure below.
Is Sara's figure a parallelogram? Why or why not?

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Problem 705

$isosceles\ triangles$ $equilateral\ triangles$ $Right\ triangles$
2. Use your knowledge of angle properties to identify the angles. /12 $180^\circ - 45^\circ = 135^\circ$ $180^\circ$ $45^\circ$ $180^\circ$ $42^\circ$ $94^\circ$ $44^\circ$ $42^\circ$ $122^\circ$ $42^\circ$ $41^\circ$ $35^\circ$ A $45^\circ$ B $135^\circ$ C D E F G H I J K L

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Problem 706

8. Error analysis: describe and correct the error in describing $\angle 5$ is congruent to $\angle 6$ .

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Problem 707

For questions 9-11, find the values of x and y if $l || m$ .
9. $(10x - 17)^{\circ}$ $(6y + 29)^{\circ}$ $(8x + 1)^{\circ}$
10. $(3y + 11)^{\circ}$ $(7x - 30)^{\circ}$ $(5x + 14)^{\circ}$
11. $(7y - 23)^{\circ}$ $(23x - 16)^{\circ}$ $(8x - 21)^{\circ}$

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Problem 708

Convert the angle to D°M'S'' form.
$48.42^\circ$
$48.42^\circ = \Box^\circ \Box' \Box ''$
(Round to the nearest second as needed.)

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Problem 709

What angle does the line $y=\frac{\sqrt{3}}{3} x+3$ form with the positive side of the line $y=3$ ?

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Problem 710

Find $m \angle L F K$ if $\overrightarrow{F K}$ bisects $\angle J F L$ and $m \angle J F L = 90^{\circ}$ .

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Problem 711

Find the angle measures of a triangle where $m \angle P=(x+5)^{\circ}$ , $m \angle Q=(2x+4)^{\circ}$ , $m \angle R=(6x)^{\circ}$ .

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Problem 712

Find two supplementary angles where the difference is $35^{\circ}$ .

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Problem 713

Video questions answered $\overleftrightarrow{D F}$ and $\overleftrightarrow{G I}$ are parallel lines. 154 Smartscore out of 1008 54 ใ요요
Which angles are corresponding angles? $\angle I H E$ and $\angle F E H$ $\angle F E C$ and $\angle I H J$ $\angle G H E$ and $\angle D E H$ $\angle G H J$ and $\angle D E H$ Type here to search 68F Light rain

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Problem 714

In the diagram, $a \perp b$ . Find the value of $x$ that makes $b||c$ .
$c$ $a$ $b$ $(9x + 18)^{\circ}$ $x =$

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Problem 715

In the figure below, $m\angle MKJ = 128^\circ$ .
$48^\circ$ $(5x)^\circ$
(a) Write an equation to find $x$ . Make sure you use an "=" sign in your answer. Equation:
(b) Solve for $x$ . $x =$

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Problem 716

Find the distance between two cars below a 1000-foot cliff with angles of depression $21^{\circ}$ and $28^{\circ}$ . Round to $0.1 \mathrm{ft}$ .

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Problem 717

Find the measure of $\angle 2$ if $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ .

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Problem 718

In triangle $ACE$ , $AD$ and $EB$ are altitudes. Given $\angle CAE=82^\circ$ and $\angle AEC=47^\circ$ , find $\angle AFE$ .

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Problem 719

In triangle $ACE$ , given $\angle CAE=82^{\circ}$ and $\angle AEC=47^{\circ}$ , find $\angle AFE$ .

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Problem 720

Find the number of sides $n$ in a polygon with exterior angles $65^{\circ}$ , $85^{\circ}$ , and remaining interior angles $150^{\circ}$ .

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Problem 721

Question What is the positive radian measure of the larger angle formed by the hands of a clock at 2 o'clock? Simplify your answer completely. Answer Attempt 3 out of 3

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Problem 722

Solve for $x$ $x=\square$

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Problem 723

X = 2x° 86°

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Problem 724

What is the measure of $\angle$ ADC in quadrilateral ABCD? $45^\circ$ $65^\circ$ $115^\circ$ $135^\circ$

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Problem 725

Find $\angle DBA$ and $\angle ABC$ if ray $BD$ bisects $\angle ABC$ and $\angle CBA = (4x + 24)^\circ$ .

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Problem 726

ement PROOF In Exercises 13 and 14, write a two-column provi. (See Examnle 4.)
13. Given $\angle G F H \cong \angle G H F$
Prove $\angle E F G$ and $\angle G H F$ are suppiementary.
14. Given $\frac{\overrightarrow{A B}}{\stackrel{B F}{F}} \equiv \overline{F G}$ , Prove $\overline{B C} \cong \overline{D F}$ $\qquad$

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Problem 727

Lines $f$ and $h$ are parallel and intersected by line $q$ , as shown.
Select statements and a reason to complete the proof showing $\angle 3 \cong \angle 6$ .

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Problem 728

Complete the table below to determine the complement and supplement of eacit angle measure \begin{tabular}{|c|l|l|} \cline { 2 - 3 } \multicolumn{1}{c|}{} & COMPLEMENT & SUPPLEMENT \\ \hline $m \angle R=102^{\circ}$ & & \\ \hline $m \angle S=73^{\circ}$ & & \\ \hline $m \angle T=41.5^{\circ}$ & & \\ \hline \end{tabular}

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Problem 729

Determine if the angle $\frac{3 \pi}{4}$ is acute or obtuse.

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Problem 730

Are the angles $330^{\circ}$ and $-240^{\circ}$ coterminal? Answer Yes or No.

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Problem 731

Find the angles: $m \angle E F H = (5x + 1)^\circ$ , $m \angle H F G = 62^\circ$ , $m \angle E F G = (18x + 11)^\circ$ .

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Problem 732

1. Answer the following about the angles: a) Vertex of $\angle 4$ ? b) Sides of $\angle 1$ ? c) Another name for $\angle 5$ ? d) Classify: $\angle F B C$ , $\angle E B F$ , $\angle A B C$ . e) Name an angle bisector. f) If $m \angle E B D=36^{\circ}$ and $m \angle D B C=108^{\circ}$ , find $m \angle E B C$ .

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Problem 733

Given $\overrightarrow{B F} \perp \overleftrightarrow{A C}$ , answer these: a) Vertex of $\angle 4 . \angle E$ ? b) Sides of $\angle 1$ ? c) Another name for $\angle 5$ ? d) Classify: $\angle F B C$ , $\angle E B F$ , $\angle A B C$ ? e) Name an angle bisector. f) If $m \angle E B D=36^{\circ}$ and $m \angle D B C=108^{\circ}$ , find $m \angle E B C$ . g) If $m \angle E B F=117^{\circ}$ , find $m \angle A B E$ .

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Problem 734

Identify the hypothesis in the statement: "If an angle measures $30^{\circ}$ , then it is an acute angle."

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Problem 735

Find the measures of angles RST, RSU, and UST given $m \angle RST=(12x-1)^{\circ}$ , $m \angle RSU=(9x-15)^{\circ}$ , and $m \angle UST=53^{\circ}$ .

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Problem 736

If an angle is $30^{\circ}$ , then it is an acute angle.

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Problem 737

Find the measures of angles $W X Z$ and $Z X Y$ given $m \angle W X Z=(5 x+3)^{\circ}$ , $m \angle Z X Y=(8 x-4)^{\circ}$ , and $\angle W X Y$ is a right angle.

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Problem 738

An angle is a right angle if and only if its measure is $90^{\circ}$ .

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Problem 739

In an isosceles triangle, the larger angle is 16 times each of the other two angles. What is the measure of the larger angle?

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Problem 740

Prove that if $\angle ABC$ and $\angle CBD$ are a linear pair, then they are supplementary.

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Problem 741

If $\angle \mathrm{ABC}$ and $\angle \mathrm{DEF}$ are supplementary, and $\angle \mathrm{ABC}$ and $\angle \mathrm{GHJ}$ are also supplementary, what can you conclude? Choose the correct answer: A. $\mathrm{m} \angle \mathrm{DEF}=\mathrm{m} \angle \mathrm{GHJ}$ B. $m \angle D E F+m \angle G H J=180$ C. $m \angle A B C=m \angle D E F$ and $m \angle A B C=m \angle G H J$ D. $m \angle D E F+m \angle G H J=90$

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Problem 742

Find $k$ for the line through $(2,-3)$ and $(k, 1)$ to be a. parallel to $5x + 3y = 6$ , b. perpendicular to $4x - 5y = -1$ .

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Problem 743

You are shown $\angle V W X$ below whose measure is $68^{\circ}$ . Draw an angle bisector of $\angle V W X$ by clicking a dragging a ray out from the vertex at $W$ .
Click and drag to draw a ray from the yellow dot. To redraw, click and drag from the yellow dot again. $\mathrm{m} \angle \mathrm{vWX}=68^{\circ}$

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Problem 744

Find the value of $x$ . 9

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Problem 745

What is the angle between the vectors $\mathbf{u}=\left[\begin{array}{l}2 \\ 0 \\ 0 \\ 0\end{array}\right]$ and $\mathbf{v}=\left[\begin{array}{l}1 \\ 0 \\ 1 \\ 0\end{array}\right]$ ? a) 0 b) $\pi / 6$ c) $\pi / 4$ d) $\pi / 3$ e) $\pi / 2$

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Problem 746

(4) The sum of 2 interior angles of a regular polygon sum to $216^{\circ}$ . How many sides does this polygon have?

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Problem 747

Rewrite the converse and biconditional for these true statements:
8. If point $B$ is on $\overline{A C}$ , then $A B + B C = A C$ .
9. If two angles are right, then they are congruent.
10. If an angle is between 90 and 180 degrees, then it is obtuse.
11. If an angle is 90 degrees, then it is a right angle.

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Problem 748

Prove the Linear Pairs Theorem: If $\angle ABC$ and $\angle CBD$ are a linear pair, then they are supplementary.

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Problem 749

A camp counselor needs to find length $x$ in feet across a lake. Given lengths: $AB = 1800$ , $EB = 1400$ , $BD = 700$ , $CD = 800$ . Find $x$ .

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Problem 750

Find the measures of complementary angles $\angle J$ and $\angle K$ , where $\angle J$ is 18 less than $\angle K$ .

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Problem 751

In triangle $XYZ$ , angle $YXZ$ is $50^{\circ}$ and angle $XYZ$ is $75^{\circ}$ . Find angle $XZY$ in degrees.

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Problem 752

8. What is the name of this angle? $<$ HSN $<\mathrm{NSH}$ $<\mathrm{SHN}$ $<\mathrm{HNS}$

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Problem 753

Which of these statements is true? $\overleftrightarrow{W X} \perp \overleftrightarrow{Z Y}$ and $\overleftrightarrow{A B}|\mid \overleftrightarrow{U V}$ $\overleftrightarrow{U V}|\mid \overleftrightarrow{A B}$ and $\overleftrightarrow{U V}| \mid \overleftrightarrow{Z Y}$ $\overleftrightarrow{W X} \perp \overleftrightarrow{Z Y}$ and $\overleftrightarrow{W X} \| \overleftrightarrow{A B}$ $\overleftrightarrow{U V} \perp \overleftrightarrow{W X}$ and $\overleftrightarrow{A B} \perp \overleftrightarrow{W X}$

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Problem 754

Use the diagram to the right to complete the statement. $\angle O R Q \cong \angle$ $\angle O R Q \cong \angle$ $\square$

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Problem 755

State two other ways to name $\angle$ z.
Two other ways to name $\angle z$ are $\square$ (Use a comma to separate answers as needed.)

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Problem 756

Find the measure of angle $X Z Y$ in triangle $X Y Z$ where angle $Y X Z = 50^{\circ}$ and angle $X Y Z = 75^{\circ}$ .

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Problem 757

Solve for the value of $q$ .

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Problem 758

6 Дана прямая призма $A B C D A_{1} B_{1} C_{1} D_{1}$ . Известно, что $A B=A C=A A_{1}, \angle B A C=90^{\circ}$ . Найдите угол между прямыми $B_{1} C$ и $A B$ .

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Problem 759

Ray BE bisects $\angle A B C$ . If $m \angle A B E=(3 x+8)^{\circ}$ and $m \angle C B E=(7 x-8)^{\circ}$ , what is $m \angle C B E ?$ $4^{\circ}$ $9^{\circ}$ $20^{\circ}$ $40^{\circ}$

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Problem 760

44. a. How do you find the sum of the interior angles of a polygon? $18(n-r)$ b. Find the value of $x$ . $\begin{array}{l} 120+2 x+65+18 \end{array}$

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Problem 761

Find the value of the variable. A. -37 B. 31 C. 43 D. 155

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Problem 762

Find $a$ and $b$ so that $(3a-27)^\circ + (2b+14)^\circ = 90^\circ$ . Round to the nearest whole number.

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Problem 763

Rays BA and BC are perpendicular. Given m∠ABD=(3x+5)° and m∠DBC=(5x-27)°, find x, m∠ABD, and m∠DBC.
x= m∠ABD= m∠DBC=

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Problem 764

$m \angle x=0 u$
Prove: $m \angle 7=120^{\circ}$
Statements Reasons $m|\mid n$ $m \angle 2=60^{\circ}$ $\angle 8 \approx \angle 2$ $m \angle 8=m \angle 2$ 2 $m(8-60)$ Angle Congruence Postulate Substitution Property of Equality $m \angle 7+m \angle 8=180^{\circ}$ Linear Pair Postulate

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Problem 765

In parallelogram EFGH, the measure of angle $F$ is $(3 x-10)^{\circ}$ and the measure of angle $G$ is $(5 x+22)^{\circ}$ . What is the measure of angle $G$ ? $42^{\prime \prime}$ $53^{\circ}$ $117^{\circ}$ $127^{\circ}$

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Problem 766

Lessons Assessments Gradebook
Question 1 (Multiple Choice Worth 1 points) (01.06 LC)
Which of the following explains the relationship between angles C and D? Adjacent angles Corresponding angles Complementary angles Vertical angles

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Problem 767

Find $m$ if $m \angle A B C=(3m-15)^{\circ}$ and $m \angle A B D=(5m+59)^{\circ}$ are supplementary.

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Problem 768

Rays BA and BC are perpendicular. Given $m \angle ABD=(3x+5)^\circ$ and $m \angle DBC=(5x-27)^\circ$ , find $x$ , $m \angle ABD$ , and $m \angle DBC$ .
$x=$ $m \angle ABD=$ $m \angle DBC=$

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Problem 769

Given a polygon $P$ with angles 125, 35, 250, 80, 135°, identify true statements for any scaled copy $Q$ of $P$ .

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Problem 770

Find $m \angle E B F$ if $m \angle E B C=3r+10$ and $m \angle A B E=2r-20$ .

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Problem 771

Find the bearing of an airplane at $(-5,-5)$ from the origin. Provide the bearing as a single angle measure.

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Problem 772

Given: $\overline{A F} \cong \overline{F C}, \angle A B E \cong \angle E B C$ Which line is the angle bisector?

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Problem 773

Find the complement of an angle measuring $39^{\circ} 1650^{\prime \prime}$ .

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Problem 774

Find the value of $x$ . a) the sum of interior quadrilateral is 360. $x=$ $\qquad$

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Problem 775

CONSTRUCTION Lupita is building a gate following this diagram.
If $m \angle L M N=43^{\circ}$ and $\angle L M N \cong \angle O M P$ , what is $m \angle N M P$ ? A) $47^{\circ}$ B) $69^{\circ}$ C) $94^{\circ}$ D) $137^{\circ}$

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Problem 776

Find the angles: $m \angle C D F=(3x+14)^\circ$ , $m \angle F D E=(5x-2)^\circ$ , $m \angle C D E=(10x-18)^\circ$ .

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Problem 777

Find the angles: $m \angle C D F = (3x + 14)^\circ$ , $m \angle F D E = (5x - 2)^\circ$ , $m \angle C D E = (10x - 18)^\circ$ . Solve for $x$ and each angle. Also, find $m \angle L M P$ if it's 11 degrees more than $m \angle N M P$ and $m \angle N M L = 137^\circ$ .

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1 ...5 6 7 8

Angles

Problem 701

Find m∠TU1m \angle T U 1m∠TU1 if m∠TU1=2x+43m \angle T U 1=2x+43m∠TU1=2x+43, m∠IUV=135∘m \angle I U V=135^\circm∠IUV=135∘, and m∠TUV=x+178m \angle T U V=x+178m∠TUV=x+178.

Problem 702

If ∠A\angle A∠A complements ∠B\angle B∠B and m∠A=36∘m \angle A=36^{\circ}m∠A=36∘, find m∠Bm \angle Bm∠B.

Problem 703

Find the measure of angle C if it supplements angle D, where m∠D=117∘m \angle D = 117^{\circ}m∠D=117∘.

Problem 704

Sara was asked to drawn a parallelogram. She drew the figure below.Is Sara's figure a parallelogram? Why or why not?

Problem 705

Problem 706

8. Error analysis: describe and correct the error in describing ∠5 \angle 5 ∠5 is congruent to ∠6 \angle 6 ∠6.

Problem 707

Problem 708

Convert the angle to D°M'S'' form.48.42∘48.42^\circ48.42∘48.42∘=□∘□′□′′48.42^\circ = \Box^\circ \Box' \Box ''48.42∘=□∘□′□′′(Round to the nearest second as needed.)

Problem 709

What angle does the line y=33x+3y=\frac{\sqrt{3}}{3} x+3y=33​​x+3 form with the positive side of the line y=3y=3y=3?

Problem 710

Find m∠LFKm \angle L F Km∠LFK if FKundefined\overrightarrow{F K}FK bisects ∠JFL\angle J F L∠JFL and m∠JFL=90∘m \angle J F L = 90^{\circ}m∠JFL=90∘.

Problem 711

Find the angle measures of a triangle where m∠P=(x+5)∘m \angle P=(x+5)^{\circ}m∠P=(x+5)∘, m∠Q=(2x+4)∘m \angle Q=(2x+4)^{\circ}m∠Q=(2x+4)∘, m∠R=(6x)∘m \angle R=(6x)^{\circ}m∠R=(6x)∘.

Problem 712

Find two supplementary angles where the difference is 35∘35^{\circ}35∘.

Problem 713

Problem 714

In the diagram, a⊥ba \perp ba⊥b. Find the value of xxx that makes b∣∣cb||cb∣∣c.ccc aaa bbb (9x+18)∘(9x + 18)^{\circ}(9x+18)∘ x=x =x=

Problem 715

In the figure below, m∠MKJ=128∘m\angle MKJ = 128^\circm∠MKJ=128∘.48∘48^\circ48∘ (5x)∘(5x)^\circ(5x)∘(a) Write an equation to find xxx. Make sure you use an "=" sign in your answer. Equation:(b) Solve for xxx. x=x = x=

Problem 716

Find the distance between two cars below a 1000-foot cliff with angles of depression 21∘21^{\circ}21∘ and 28∘28^{\circ}28∘. Round to 0.1ft0.1 \mathrm{ft}0.1ft.

Problem 717

Find the measure of ∠2\angle 2∠2 if m∠1=(2x+29)∘\mathrm{m} \angle 1=(2 x+29)^{\circ}m∠1=(2x+29)∘ and m∠2=(3x−17)∘\mathrm{m} \angle 2=(3 x-17)^{\circ}m∠2=(3x−17)∘.

Problem 718

In triangle ACEACEACE, ADADAD and EBEBEB are altitudes. Given ∠CAE=82∘\angle CAE=82^\circ∠CAE=82∘ and ∠AEC=47∘\angle AEC=47^\circ∠AEC=47∘, find ∠AFE\angle AFE∠AFE.

Problem 719

In triangle ACEACEACE, given ∠CAE=82∘\angle CAE=82^{\circ}∠CAE=82∘ and ∠AEC=47∘\angle AEC=47^{\circ}∠AEC=47∘, find ∠AFE\angle AFE∠AFE.

Problem 720

Find the number of sides nnn in a polygon with exterior angles 65∘65^{\circ}65∘, 85∘85^{\circ}85∘, and remaining interior angles 150∘150^{\circ}150∘.

Problem 721

Question What is the positive radian measure of the larger angle formed by the hands of a clock at 2 o'clock? Simplify your answer completely. Answer Attempt 3 out of 3

Problem 722

Solve for xxx x=□x=\squarex=□

Problem 723

X = 2x° 86°

Problem 724

What is the measure of ∠\angle∠ADC in quadrilateral ABCD? 45∘45^\circ45∘ 65∘65^\circ65∘ 115∘115^\circ115∘ 135∘135^\circ135∘

Problem 725

Find ∠DBA\angle DBA∠DBA and ∠ABC\angle ABC∠ABC if ray BDBDBD bisects ∠ABC\angle ABC∠ABC and ∠CBA=(4x+24)∘\angle CBA = (4x + 24)^\circ∠CBA=(4x+24)∘.

Problem 726

Problem 727

Lines fff and hhh are parallel and intersected by line qqq, as shown.Select statements and a reason to complete the proof showing ∠3≅∠6\angle 3 \cong \angle 6∠3≅∠6.

Problem 728

Problem 729

Determine if the angle 3π4\frac{3 \pi}{4}43π​ is acute or obtuse.

Problem 730

Are the angles 330∘330^{\circ}330∘ and −240∘-240^{\circ}−240∘ coterminal? Answer Yes or No.

Problem 731

Find the angles: m∠EFH=(5x+1)∘m \angle E F H = (5x + 1)^\circm∠EFH=(5x+1)∘, m∠HFG=62∘m \angle H F G = 62^\circm∠HFG=62∘, m∠EFG=(18x+11)∘m \angle E F G = (18x + 11)^\circm∠EFG=(18x+11)∘.

Problem 732

Problem 733

Problem 734

Identify the hypothesis in the statement: "If an angle measures 30∘30^{\circ}30∘, then it is an acute angle."

Problem 735

Find the measures of angles RST, RSU, and UST given m∠RST=(12x−1)∘m \angle RST=(12x-1)^{\circ}m∠RST=(12x−1)∘, m∠RSU=(9x−15)∘m \angle RSU=(9x-15)^{\circ}m∠RSU=(9x−15)∘, and m∠UST=53∘m \angle UST=53^{\circ}m∠UST=53∘.

Problem 736

If an angle is 30∘30^{\circ}30∘, then it is an acute angle.

Problem 737

Find the measures of angles WXZW X ZWXZ and ZXYZ X YZXY given m∠WXZ=(5x+3)∘m \angle W X Z=(5 x+3)^{\circ}m∠WXZ=(5x+3)∘, m∠ZXY=(8x−4)∘m \angle Z X Y=(8 x-4)^{\circ}m∠ZXY=(8x−4)∘, and ∠WXY\angle W X Y∠WXY is a right angle.

Problem 738

An angle is a right angle if and only if its measure is 90∘90^{\circ}90∘.

Problem 739

In an isosceles triangle, the larger angle is 16 times each of the other two angles. What is the measure of the larger angle?

Problem 740

Prove that if ∠ABC\angle ABC∠ABC and ∠CBD\angle CBD∠CBD are a linear pair, then they are supplementary.

Problem 741

Problem 742

Find kkk for the line through (2,−3)(2,-3)(2,−3) and (k,1)(k, 1)(k,1) to be a. parallel to 5x+3y=65x + 3y = 65x+3y=6, b. perpendicular to 4x−5y=−14x - 5y = -14x−5y=−1.

Problem 743

Problem 744

Find the value of xxx. 9

Find $m \angle T U 1$ if $m \angle T U 1=2x+43$ , $m \angle I U V=135^\circ$ , and $m \angle T U V=x+178$ .

If $\angle A$ complements $\angle B$ and $m \angle A=36^{\circ}$ , find $m \angle B$ .

Find the measure of angle C if it supplements angle D, where $m \angle D = 117^{\circ}$ .

Sara was asked to drawn a parallelogram. She drew the figure below.
Is Sara's figure a parallelogram? Why or why not?

8. Error analysis: describe and correct the error in describing $\angle 5$ is congruent to $\angle 6$ .

Convert the angle to D°M'S'' form.
$48.42^\circ$
$48.42^\circ = \Box^\circ \Box' \Box ''$
(Round to the nearest second as needed.)

What angle does the line $y=\frac{\sqrt{3}}{3} x+3$ form with the positive side of the line $y=3$ ?

Find $m \angle L F K$ if $\overrightarrow{F K}$ bisects $\angle J F L$ and $m \angle J F L = 90^{\circ}$ .

Find the angle measures of a triangle where $m \angle P=(x+5)^{\circ}$ , $m \angle Q=(2x+4)^{\circ}$ , $m \angle R=(6x)^{\circ}$ .

Find two supplementary angles where the difference is $35^{\circ}$ .

In the diagram, $a \perp b$ . Find the value of $x$ that makes $b||c$ .
$c$ $a$ $b$ $(9x + 18)^{\circ}$ $x =$

In the figure below, $m\angle MKJ = 128^\circ$ .
$48^\circ$ $(5x)^\circ$
(a) Write an equation to find $x$ . Make sure you use an "=" sign in your answer. Equation:
(b) Solve for $x$ . $x =$

Find the distance between two cars below a 1000-foot cliff with angles of depression $21^{\circ}$ and $28^{\circ}$ . Round to $0.1 \mathrm{ft}$ .

Find the measure of $\angle 2$ if $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ .

In triangle $ACE$ , $AD$ and $EB$ are altitudes. Given $\angle CAE=82^\circ$ and $\angle AEC=47^\circ$ , find $\angle AFE$ .

In triangle $ACE$ , given $\angle CAE=82^{\circ}$ and $\angle AEC=47^{\circ}$ , find $\angle AFE$ .

Find the number of sides $n$ in a polygon with exterior angles $65^{\circ}$ , $85^{\circ}$ , and remaining interior angles $150^{\circ}$ .

Solve for $x$ $x=\square$

What is the measure of $\angle$ ADC in quadrilateral ABCD? $45^\circ$ $65^\circ$ $115^\circ$ $135^\circ$

Find $\angle DBA$ and $\angle ABC$ if ray $BD$ bisects $\angle ABC$ and $\angle CBA = (4x + 24)^\circ$ .

Lines $f$ and $h$ are parallel and intersected by line $q$ , as shown.
Select statements and a reason to complete the proof showing $\angle 3 \cong \angle 6$ .

Determine if the angle $\frac{3 \pi}{4}$ is acute or obtuse.

Are the angles $330^{\circ}$ and $-240^{\circ}$ coterminal? Answer Yes or No.

Find the angles: $m \angle E F H = (5x + 1)^\circ$ , $m \angle H F G = 62^\circ$ , $m \angle E F G = (18x + 11)^\circ$ .

Identify the hypothesis in the statement: "If an angle measures $30^{\circ}$ , then it is an acute angle."

Find the measures of angles RST, RSU, and UST given $m \angle RST=(12x-1)^{\circ}$ , $m \angle RSU=(9x-15)^{\circ}$ , and $m \angle UST=53^{\circ}$ .

If an angle is $30^{\circ}$ , then it is an acute angle.

Find the measures of angles $W X Z$ and $Z X Y$ given $m \angle W X Z=(5 x+3)^{\circ}$ , $m \angle Z X Y=(8 x-4)^{\circ}$ , and $\angle W X Y$ is a right angle.

An angle is a right angle if and only if its measure is $90^{\circ}$ .

Prove that if $\angle ABC$ and $\angle CBD$ are a linear pair, then they are supplementary.

Find $k$ for the line through $(2,-3)$ and $(k, 1)$ to be a. parallel to $5x + 3y = 6$ , b. perpendicular to $4x - 5y = -1$ .

Find the value of $x$ . 9

(4) The sum of 2 interior angles of a regular polygon sum to $216^{\circ}$ . How many sides does this polygon have?

Prove the Linear Pairs Theorem: If $\angle ABC$ and $\angle CBD$ are a linear pair, then they are supplementary.

A camp counselor needs to find length $x$ in feet across a lake. Given lengths: $AB = 1800$ , $EB = 1400$ , $BD = 700$ , $CD = 800$ . Find $x$ .

Find the measures of complementary angles $\angle J$ and $\angle K$ , where $\angle J$ is 18 less than $\angle K$ .

In triangle $XYZ$ , angle $YXZ$ is $50^{\circ}$ and angle $XYZ$ is $75^{\circ}$ . Find angle $XZY$ in degrees.

8. What is the name of this angle? $<$ HSN $<\mathrm{NSH}$ $<\mathrm{SHN}$ $<\mathrm{HNS}$

Use the diagram to the right to complete the statement. $\angle O R Q \cong \angle$ $\angle O R Q \cong \angle$ $\square$

State two other ways to name $\angle$ z.
Two other ways to name $\angle z$ are $\square$ (Use a comma to separate answers as needed.)

Find the measure of angle $X Z Y$ in triangle $X Y Z$ where angle $Y X Z = 50^{\circ}$ and angle $X Y Z = 75^{\circ}$ .

Solve for the value of $q$ .

6 Дана прямая призма $A B C D A_{1} B_{1} C_{1} D_{1}$ . Известно, что $A B=A C=A A_{1}, \angle B A C=90^{\circ}$ . Найдите угол между прямыми $B_{1} C$ и $A B$ .

44. a. How do you find the sum of the interior angles of a polygon? $18(n-r)$ b. Find the value of $x$ . $\begin{array}{l} 120+2 x+65+18 \end{array}$

Find $a$ and $b$ so that $(3a-27)^\circ + (2b+14)^\circ = 90^\circ$ . Round to the nearest whole number.

Rays BA and BC are perpendicular. Given m∠ABD=(3x+5)° and m∠DBC=(5x-27)°, find x, m∠ABD, and m∠DBC.
x= m∠ABD= m∠DBC=

Lessons Assessments Gradebook
Question 1 (Multiple Choice Worth 1 points) (01.06 LC)
Which of the following explains the relationship between angles C and D? Adjacent angles Corresponding angles Complementary angles Vertical angles

Find $m$ if $m \angle A B C=(3m-15)^{\circ}$ and $m \angle A B D=(5m+59)^{\circ}$ are supplementary.

Given a polygon $P$ with angles 125, 35, 250, 80, 135°, identify true statements for any scaled copy $Q$ of $P$ .

Find $m \angle E B F$ if $m \angle E B C=3r+10$ and $m \angle A B E=2r-20$ .

Find the bearing of an airplane at $(-5,-5)$ from the origin. Provide the bearing as a single angle measure.

Given: $\overline{A F} \cong \overline{F C}, \angle A B E \cong \angle E B C$ Which line is the angle bisector?

Find the complement of an angle measuring $39^{\circ} 1650^{\prime \prime}$ .

Find the value of $x$ . a) the sum of interior quadrilateral is 360. $x=$ $\qquad$