3.2: Angles of Triangles

What are Interior and Exterior Angles

Interior Angles are angles inside a polygon.

When the sides of a polygon are extended, other angles are formed. Exterior Angles are the

angles outside of the polygon that are adjacent to the interior angles.

Interior Angles Measures of a Triangle

The sum of the interior angle measures of a triangle is 1800

Algebra x+y+z=180

Using Interior Angle Measures

Find the value of x.

Practice

43+x+x-35=180

2x+8=180

2x=172

x=860

81+25+x=180

106+x=180

x=740

Find the value of x.

Exterior Angle Measures of a Triangle

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Algebra z=x+y

Finding Exterior Angle Measures

Find the measure of the exterior angle.

Practice

4n-20=n+2n+20

4n-20=3n+20

n-20=20

n=40

Exterior angle= 4(40)-20=160-20=1400

y=40+30

y=700

Find the measure of the exterior angle.

Real Life Application

An airplane leaves from Miami and travels around the Bermuda Triangle. What is the value of x?

Use what you know about the interior angle measures of a triangle to write an equation.