Math / Geometry

Question19. Define the following terms: interior angle, exterior angle, remote interior angle, complementary angles, supplementary angles
20. Draw an example of each triangle and include the measure of each angle in your examples: acute triangle, equilateral triangle, right triangle, obtuse triangle.

Studdy Solution

STEP 1

What is this asking? We need to define some angle terms and draw labeled examples of different types of triangles. Watch out! Don't mix up the different types of angles and triangles!
Make sure your labeled drawings are neat and clear.

STEP 2

1. Define Angle Terms
2. Draw Triangles

STEP 3

Alright, let's define these angle terms!
An interior angle is an angle inside a polygon formed by two adjacent sides.
Think of it like the angles inside the corners of a shape!

STEP 4

An exterior angle is an angle formed by one side of a polygon and the extension of an adjacent side.
It's like the angle outside the corner, if you kept one side going!

STEP 5

A remote interior angle is an interior angle of a triangle that is not adjacent to a given exterior angle.
So, if you pick an exterior angle, the two interior angles on the opposite side of the triangle are its remote interior angles.

STEP 6

Complementary angles are two angles whose measures add up to $90^\circ$ .
Think of a right angle being split into two parts!

STEP 7

Supplementary angles are two angles whose measures add up to $180^\circ$ .
Think of a straight line being split into two angles!

STEP 8

An acute triangle has all interior angles measuring less than $90^\circ$ .
Let's draw one with angles $50^\circ$ , $60^\circ$ , and $70^\circ$ .
Notice how $50^\circ + 60^\circ + 70^\circ = 180^\circ$ !
All angles are less than $90^\circ$ and they add up to $180^\circ$ , just like the angles in any triangle should!

STEP 9

An equilateral triangle has all sides equal in length, and all angles equal to $60^\circ$ .
So, let's draw one with all angles labeled $60^\circ$ ! $60^\circ + 60^\circ + 60^\circ = 180^\circ$ , perfect!

STEP 10

A right triangle has one angle that measures exactly $90^\circ$ .
Let's draw one with angles $30^\circ$ , $60^\circ$ , and $90^\circ$ . $30^\circ + 60^\circ + 90^\circ = 180^\circ$ , awesome!

STEP 11

An obtuse triangle has one angle that measures greater than $90^\circ$ .
Let's draw one with angles $30^\circ$ , $40^\circ$ , and $110^\circ$ . $30^\circ + 40^\circ + 110^\circ = 180^\circ$ , fantastic!

STEP 12

We've defined interior angle, exterior angle, remote interior angle, complementary angles, and supplementary angles.
We've also drawn and labeled an acute, equilateral, right, and obtuse triangle, with the measure of each angle included!

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Studdy Solution

STEP 1

What is this asking? We need to define some angle terms and draw labeled examples of different types of triangles. Watch out! Don't mix up the different types of angles and triangles!
Make sure your labeled drawings are neat and clear.

STEP 2

1. Define Angle Terms
2. Draw Triangles

STEP 3

Alright, let's define these angle terms!
An interior angle is an angle inside a polygon formed by two adjacent sides.
Think of it like the angles inside the corners of a shape!

STEP 4

An exterior angle is an angle formed by one side of a polygon and the extension of an adjacent side.
It's like the angle outside the corner, if you kept one side going!

STEP 5

A remote interior angle is an interior angle of a triangle that is not adjacent to a given exterior angle.
So, if you pick an exterior angle, the two interior angles on the opposite side of the triangle are its remote interior angles.

STEP 6

Complementary angles are two angles whose measures add up to $90^\circ$ .
Think of a right angle being split into two parts!

STEP 7

Supplementary angles are two angles whose measures add up to $180^\circ$ .
Think of a straight line being split into two angles!

STEP 8

STEP 9

An equilateral triangle has all sides equal in length, and all angles equal to $60^\circ$ .
So, let's draw one with all angles labeled $60^\circ$ ! $60^\circ + 60^\circ + 60^\circ = 180^\circ$ , perfect!

STEP 10

A right triangle has one angle that measures exactly $90^\circ$ .
Let's draw one with angles $30^\circ$ , $60^\circ$ , and $90^\circ$ . $30^\circ + 60^\circ + 90^\circ = 180^\circ$ , awesome!

STEP 11

An obtuse triangle has one angle that measures greater than $90^\circ$ .
Let's draw one with angles $30^\circ$ , $40^\circ$ , and $110^\circ$ . $30^\circ + 40^\circ + 110^\circ = 180^\circ$ , fantastic!

STEP 12

We've defined interior angle, exterior angle, remote interior angle, complementary angles, and supplementary angles.
We've also drawn and labeled an acute, equilateral, right, and obtuse triangle, with the measure of each angle included!

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Studdy Solution

STEP 1

What is this asking? We need to define some angle terms and draw labeled examples of different types of triangles. Watch out! Don't mix up the different types of angles and triangles!Make sure your labeled drawings are neat and clear.

STEP 2

1. Define Angle Terms2. Draw Triangles

STEP 3

Alright, let's **define** these angle terms!An *interior angle* is an angle inside a polygon formed by two adjacent sides.Think of it like the angles *inside* the corners of a shape!

STEP 4

An *exterior angle* is an angle formed by one side of a polygon and the extension of an adjacent side.It's like the angle *outside* the corner, if you kept one side going!

STEP 5

A *remote interior angle* is an interior angle of a triangle that is not adjacent to a given exterior angle.So, if you pick an exterior angle, the two interior angles on the *opposite* side of the triangle are its remote interior angles.

STEP 6

*Complementary angles* are two angles whose measures add up to 90∘90^\circ90∘.Think of a right angle being split into two parts!

STEP 7

*Supplementary angles* are two angles whose measures add up to 180∘180^\circ180∘.Think of a straight line being split into two angles!

STEP 8

STEP 9

An *equilateral triangle* has all sides equal in length, and all angles equal to 60∘60^\circ60∘.So, let's draw one with all angles labeled 60∘60^\circ60∘! 60∘+60∘+60∘=180∘60^\circ + 60^\circ + 60^\circ = 180^\circ60∘+60∘+60∘=180∘, perfect!

STEP 10

A *right triangle* has one angle that measures exactly 90∘90^\circ90∘.Let's draw one with angles 30∘30^\circ30∘, 60∘60^\circ60∘, and 90∘90^\circ90∘. 30∘+60∘+90∘=180∘30^\circ + 60^\circ + 90^\circ = 180^\circ30∘+60∘+90∘=180∘, awesome!

STEP 11

An *obtuse triangle* has one angle that measures greater than 90∘90^\circ90∘.Let's draw one with angles 30∘30^\circ30∘, 40∘40^\circ40∘, and 110∘110^\circ110∘. 30∘+40∘+110∘=180∘30^\circ + 40^\circ + 110^\circ = 180^\circ30∘+40∘+110∘=180∘, fantastic!

STEP 12

We've defined *interior angle*, *exterior angle*, *remote interior angle*, *complementary angles*, and *supplementary angles*.We've also drawn and labeled an *acute*, *equilateral*, *right*, and *obtuse* triangle, with the measure of each angle included!

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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.

What is this asking? We need to define some angle terms and draw labeled examples of different types of triangles. Watch out! Don't mix up the different types of angles and triangles!
Make sure your labeled drawings are neat and clear.

1. Define Angle Terms
2. Draw Triangles

Alright, let's define these angle terms!
An interior angle is an angle inside a polygon formed by two adjacent sides.
Think of it like the angles inside the corners of a shape!

An exterior angle is an angle formed by one side of a polygon and the extension of an adjacent side.
It's like the angle outside the corner, if you kept one side going!

A remote interior angle is an interior angle of a triangle that is not adjacent to a given exterior angle.
So, if you pick an exterior angle, the two interior angles on the opposite side of the triangle are its remote interior angles.

Complementary angles are two angles whose measures add up to $90^\circ$ .
Think of a right angle being split into two parts!

Supplementary angles are two angles whose measures add up to $180^\circ$ .
Think of a straight line being split into two angles!

An equilateral triangle has all sides equal in length, and all angles equal to $60^\circ$ .
So, let's draw one with all angles labeled $60^\circ$ ! $60^\circ + 60^\circ + 60^\circ = 180^\circ$ , perfect!

A right triangle has one angle that measures exactly $90^\circ$ .
Let's draw one with angles $30^\circ$ , $60^\circ$ , and $90^\circ$ . $30^\circ + 60^\circ + 90^\circ = 180^\circ$ , awesome!

An obtuse triangle has one angle that measures greater than $90^\circ$ .
Let's draw one with angles $30^\circ$ , $40^\circ$ , and $110^\circ$ . $30^\circ + 40^\circ + 110^\circ = 180^\circ$ , fantastic!

We've defined interior angle, exterior angle, remote interior angle, complementary angles, and supplementary angles.
We've also drawn and labeled an acute, equilateral, right, and obtuse triangle, with the measure of each angle included!