Exterior Angle Theorem Notes

ACTIVITY

INSTRUCTION:

Arrange the jumbled letters to identify the word being described.

Fill in the Blanks

L E R A G T I N

"It is a polygon with three sides, three angles, and three vertices."

Multiple Select

Which of the following is NOT A TRIANGLE?

Fill in the Blanks

G R I T H

"It is an angle that is exactly 90 degrees."

Multiple Choice

Which of the following illustrates a RIGHT ANGLE?

Fill in the Blanks

T U C E A

"It is an angle that measures less than 90 degrees."

Multiple Choice

Which of the following is an ACUTE angle?

Fill in the Blanks

B U T E S O

"It is an angle that measures more than 90 degrees."

Multiple Select

Which of the following is an OBTUSE angle?

TRIANGLE

Parts of TRIANGLE 

There are the angles at the vertices of a triangle.

Interior Angles of a Triangle

Interior Angles​
∠L, ∠N, ∠M

Triangle Sum Theorem

The sum of all interior angles of a triangle is always 180 degrees.

State whether the given set of angles forms a triangle.

86^o, 53^o, 41^o

State whether the given set of angles forms a triangle.

86^o, 53^o, 41^o

​Yes

86 + 53 + 41 = 180

Multiple Choice

State whether the given set of angles forms a triangle.
$$47\degree,\ 84\degree,\ 56\degree$$

• Yes

• No

Multiple Choice

State whether the given set of angles forms a triangle.
$$70\degree,\ 22\degree,\ 68\degree$$

• Yes

• No

Multiple Choice

State whether the given set of angles forms a triangle.
$$54\degree,\ 97\degree,\ 29\degree$$

• Yes

• No

Multiple Choice

State whether the given set of angles forms a triangle.
$$33\degree,\ 90\degree,\ 57\degree$$

• Yes

• No

Multiple Choice

State whether the given set of angles forms a triangle.
$$28\degree,\ 64\degree,\ 100\degree$$

• Yes

• No

Find the measure of the indicated angle in each triangle.

86 + 53 + 41 = 180

Find the value of x in the triangle.

86 + 53 + 41 = 180

86 + 53 + 41 = 180

Find the value of x in the triangle.

86 + 53 + 41 = 180

86 + 53 + 41 = 180

86 + 53 + 41 = 180

Find the value of x in the triangle.

86 + 53 + 41 = 180

86 + 53 + 41 = 180

86 + 53 + 41 = 180

86 + 53 + 41 = 180

It is the supplement to a triangle's interior angle. Supplementary angles that add to make a straight angle or straight line. 180⁰

Exterior Angles of a Triangle

​Exterior Angles:
∠a, ∠b, ∠c

Categorize

Options (6)

$$\angle a$$  

$$\angle b$$  

$$\angle c$$  

$$\angle d$$  

$$\angle e$$  

$$\angle f$$  

Classify the following angles based on their category.

Interior Angles

Exterior Angles

​Remote Interior angle

A remote interior angle is an angle of a triangle that is not adjacent to a given exterior angle.

Multiple Select

Which of the following are the remote interior angles of ∠d

• ∠a

• ∠b

• ∠c

• ∠e

• ∠f

Multiple Select

Which of the following are the remote interior angles of ∠e

• ∠a

• ∠b

• ∠c

• ∠d

• ∠f

Multiple Select

Which of the following are the remote interior angles of ∠f

• ∠a

• ∠b

• ∠c

• ∠d

• ∠e

Exterior Angle Theorem

It states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote (non-adjacent) interior angles.

Example 1:

e⁰ = 60⁰+37⁰
e⁰ = 97⁰

Given the triangle at the right, e can be solved by adding the two remote interior angles.

Fill in the Blanks

What is the d⁰ ?

Fill in the Blanks

What is the a⁰ ?

Fill in the Blanks

What is the f⁰ ?

Find the value of x in the triangle.

86 + 53 + 41 = 180

86 + 53 + 41 = 180

86 + 53 + 41 = 180

Find the value of x in the triangle.

86 + 53 + 41 = 180

86 + 53 + 41 = 180

86 + 53 + 41 = 180

Example 2:

c⁰ = 116⁰ - 58⁰
c⁰ = 58⁰

Solve for one of the remote interior angles given its exterior angle.

Fill in the Blanks

Solve for z⁰.

Fill in the Blanks

Solve for r⁰.

Example 2:

c⁰ = 116⁰ - 58⁰
c⁰ = 58⁰

Solve for one of the remote interior angles given its exterior angle.

Example 3:

Find the value of x in the given triangle at the right,

Example 3:

5x-30 = 80 + 20
5x-30 = 100
5x = 100 + 30
x = 130∕5
x = 26

Find the value of x in the given triangle at the right,

Multiple Choice

In solving for the value of x in the given triangle, what is the correct equation to be used?

• $$12x-15=75+30$$

• $$12x-15=75-30$$

• $$12x+15=75+30$$

• $$12x+15=75-30$$

Multiple Choice

In solving for the value of x in the given triangle, what is the correct equation to be used?

• $$110=70-x$$

• $$110=70+x$$

• $$110+70=x$$

• $$110-x=70$$