Math / Geometry

QuestionIn the diagram, lines $\ell$ and $m$ are cut by transversals $n$ and $\rho$ .
Part A Enter the measure of $\angle 1$ . $\square$
Part B Enter the measure of $\angle 2$ . $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the measure of two angles formed when two lines are crossed by two other lines, and we know one of the angles is $59^\circ$ . Watch out! Don't mix up which angles are equal!
Remember the relationships between angles formed by intersecting lines.

STEP 2

1. Find Angle 1
2. Find Angle 2

STEP 3

Look closely!
Angle 1 and the $59^\circ$ angle form a straight line together.
That means they're supplementary angles, and they add up to $180^\circ$ !

STEP 4

So, to find the measure of Angle 1, we subtract $59^\circ$ from $180^\circ$ .
Let's do it: $180^\circ - 59^\circ = 121^\circ$

STEP 5

Therefore, the measure of Angle 1 is $121^\circ$ .

STEP 6

Notice that Angle 2 and the $59^\circ$ angle are vertically opposite each other.

STEP 7

Vertically opposite angles are always equal!

STEP 8

That means Angle 2 also measures $59^\circ$ .

STEP 9

Part A: The measure of $\angle 1$ is $121^\circ$ . Part B: The measure of $\angle 2$ is $59^\circ$ .

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QuestionIn the diagram, lines $\ell$ and $m$ are cut by transversals $n$ and $\rho$ .
Part A Enter the measure of $\angle 1$ . $\square$
Part B Enter the measure of $\angle 2$ . $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the measure of two angles formed when two lines are crossed by two other lines, and we know one of the angles is $59^\circ$ . Watch out! Don't mix up which angles are equal!
Remember the relationships between angles formed by intersecting lines.

STEP 2

1. Find Angle 1
2. Find Angle 2

STEP 3

Look closely!
Angle 1 and the $59^\circ$ angle form a straight line together.
That means they're supplementary angles, and they add up to $180^\circ$ !

STEP 4

So, to find the measure of Angle 1, we subtract $59^\circ$ from $180^\circ$ .
Let's do it: $180^\circ - 59^\circ = 121^\circ$

STEP 5

Therefore, the measure of Angle 1 is $121^\circ$ .

STEP 6

Notice that Angle 2 and the $59^\circ$ angle are vertically opposite each other.

STEP 7

Vertically opposite angles are always equal!

STEP 8

That means Angle 2 also measures $59^\circ$ .

STEP 9

Part A: The measure of $\angle 1$ is $121^\circ$ . Part B: The measure of $\angle 2$ is $59^\circ$ .

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QuestionIn the diagram, lines ℓ\ellℓ and mmm are cut by transversals nnn and ρ\rhoρ.Part A Enter the measure of ∠1\angle 1∠1. □\square□Part B Enter the measure of ∠2\angle 2∠2. □\square□

Studdy Solution

STEP 1

What is this asking? We need to find the measure of two angles formed when two lines are crossed by two other lines, and we know one of the angles is 59∘59^\circ59∘. Watch out! Don't mix up which angles are equal!Remember the relationships between angles formed by intersecting lines.

STEP 2

1. Find Angle 12. Find Angle 2

STEP 3

Look closely!Angle 1 and the 59∘59^\circ59∘ angle form a **straight line** together.That means they're **supplementary angles**, and they add up to 180∘180^\circ180∘!

STEP 4

So, to find the measure of Angle 1, we **subtract** 59∘59^\circ59∘ from 180∘180^\circ180∘.Let's do it: 180∘−59∘=121∘180^\circ - 59^\circ = 121^\circ180∘−59∘=121∘

STEP 5

Therefore, the measure of Angle 1 is **121∘121^\circ121∘**.

STEP 6

Notice that Angle 2 and the 59∘59^\circ59∘ angle are **vertically opposite** each other.

STEP 7

Vertically opposite angles are **always equal**!

STEP 8

That means Angle 2 also measures **59∘59^\circ59∘**.

STEP 9

Part A: The measure of ∠1\angle 1∠1 is 121∘121^\circ121∘. Part B: The measure of ∠2\angle 2∠2 is 59∘59^\circ59∘.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIn the diagram, lines $\ell$ and $m$ are cut by transversals $n$ and $\rho$ .
Part A Enter the measure of $\angle 1$ . $\square$
Part B Enter the measure of $\angle 2$ . $\square$

What is this asking? We need to find the measure of two angles formed when two lines are crossed by two other lines, and we know one of the angles is $59^\circ$ . Watch out! Don't mix up which angles are equal!
Remember the relationships between angles formed by intersecting lines.

1. Find Angle 1
2. Find Angle 2

Look closely!
Angle 1 and the $59^\circ$ angle form a straight line together.
That means they're supplementary angles, and they add up to $180^\circ$ !

So, to find the measure of Angle 1, we subtract $59^\circ$ from $180^\circ$ .
Let's do it: $180^\circ - 59^\circ = 121^\circ$

Therefore, the measure of Angle 1 is $121^\circ$ .

Notice that Angle 2 and the $59^\circ$ angle are vertically opposite each other.

Vertically opposite angles are always equal!

That means Angle 2 also measures $59^\circ$ .

Part A: The measure of $\angle 1$ is $121^\circ$ . Part B: The measure of $\angle 2$ is $59^\circ$ .