1. Find the value of x in each triangle. 1. 2.
3. Two angles of a triangle measure 35° and 65°. What is the measure of the third angle?
4. Two angles of a triangle measure 25° and 45°. What is the measure of the third angle?
5. The measures of the angles of a triangle are in the ratio 2:3:3. What are the measures of the angles?
Course3, Lesson 5-4

2. ANSWERS
1. 90
2. 15
3. 100°
4. 110°
5. 45°; 67.5°; 67.5°
Course3, Lesson 5-4

3. HOW can algebraic concepts be applied to geometry?
Course3, Lesson 5-4

4. Mathematical Practices
Geometry
Extension of 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by transversal, and the angle-angle criterion for similarity of triangles.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course3, Lesson Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

5. find the measure of an interior or exterior angle of a regular polygon
Geometry To
find the measure of an interior or exterior angle of a regular polygon
Course3, Lesson 5-4.

6. polygon equiangular regular polygon
Geometry
polygon
equiangular
regular polygon
Course3, Lesson 5-4

7. Interior Angle Sum of a Polygon
Geometry
Interior Angle Sum of a Polygon
Words The sum of the measures of the interior angles of a polygon is (n – 2)180, where n represents the number of sides.
Symbols S = (n – 2)180
Course3, Lesson 5-4

8. Find the sum of the measures of the interior angles of a decagon.
Step-by-Step Example 1.
Find the sum of the measures of the interior angles of a decagon. 1
S = (n – 2) 180
Write the equation.
S = (10 – 2) 180 2
A decagon has 10 sides. Replace n with 10. 3
S = (8)180 or 1,440
Simplify.
The sum of the measures of the interior angles of a decagon
is 1,440°. 4
Need Another Example?

9. Find the sum of the measures of the interior angles of a 13-gon.
Need Another Example?
Find the sum of the measures of the interior
angles of a 13-gon.
1,980°
Answer

10. Find the sum of the measures of the angles.
Step-by-Step Example 2.
Each chamber of a bee honeycomb is a regular hexagon. Find the measure of an interior angle of a regular hexagon. 1
Find the sum of the measures of the angles.
S = (n – 2) 180
Write an equation.
S = (6 – 2) 180
Replace n with 6.
S = (4)180 or 720
Simplify. 2
The sum of the measures of the interior angles is 720°.
Divide 720 by 6, the number of interior angles, to find the measure of one interior angle. So, the measure of one interior angle of a regular hexagon is 720° ÷ 6 or 120°. 3
Need Another Example?

11. Need Another Example?
A designer is creating a new logo for a bank. The logo consists of a regular pentagon surrounded by isosceles triangles. Find the measure of an interior angle of a regular pentagon.
108°
Answer

12. Exterior Angles of a Polygon
Geometry
Exterior Angles of a Polygon
Words In a polygon, the sum of the measures of the exterior angles, one at each vertex, is 360˚
Model
Symbols
Course3, Lesson 5-4

13. Find the measure of an exterior angle in a regular hexagon.
Step-by-Step Example 3.
Find the measure of an exterior angle in a regular hexagon. 1
Let x represent the measure of each exterior angle. 2
6x = 360
Write an equation. A hexagon has 6 exterior angles. 3
x = 60
Division Property of Equality 4
So, each exterior angle of a regular hexagon measures 60°.
Need Another Example?

14. Find the measure of an exterior angle in a regular 30-gon.
Need Another Example?
Find the measure of an exterior angle in a
regular 30-gon.
12°
Answer

15. How did what you learned today help you answer the
Geometry
How did what you learned
today help you answer the
HOW can algebraic concepts be applied to geometry?
Course 3, Lesson 5-4

16. How did what you learned today help you answer the
Geometry
How did what you learned
today help you answer the
HOW can algebraic concepts be applied to geometry?
Sample answers:
You use a formula to find the sum of the interior angles of any polygon.
You can write an equation to find the measure of a missing interior or exterior angle of a polygon.
Course 3, Lesson 5-4

17. Geometry
Functions
Ratios and Proportional Relationships
Explain how to find the sum of the interior angles of a polygon when you know the number of sides of the polygon.
Course 3, Lesson 5-4