Exterior Angle Theorem

ACTIVITY

INSTRUCTION:

Arrange the jumbled letters to identify the word being described.

Multiple Select

Which of the following is NOT A TRIANGLE?

Multiple Choice

Which of the following illustrates a RIGHT ANGLE?

Multiple Choice

Which of the following is an ACUTE angle?

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.

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.

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?

• $$110=70-x$$

• $$110=70+x$$

• $$110+70=x$$

• $$110-x=70$$