1. Find the value of x.
A. 80
B. 60
C. 40
D. 20 A B C D
5-Minute Check 2

2. Splash Screen

3. You have already classified quadrilaterals. (Lesson 11–4)
Classify polygons.
Determine the sum of the measures of the interior angles of a polygon.
Then/Now

4. polygon diagonal interior angle regular polygon
A simple closed figure in a plane formed by three or more line segments
diagonal
interior angle
regular polygon
A line segment that joins two nonconsecutive vertices of a polygon
An angle formed inside of a polygon
A polygon having all sides congruent and all angles congruent
Vocabulary

5. Polygon Names Side Number Name 3 Triangle 4 Quadrilateral 5 Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon n
n-gon

6. The figure has 5 sides that only intersect at their endpoints.
Classify Polygons
Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why.
The figure has 5 sides that only intersect at their endpoints.
Answer: It is a pentagon.
Example 1

7. A B C D Classify the polygon. A. pentagon B. hexagon C. heptagon
D. octagon A B C D
Example 1

8. Concept

9. Find the sum of the measures of the interior angles of a heptagon.
Read the Test Item
The sum of the measures of the interior angles is (n – 2)180. Since a heptagon has 7 sides, n = 7.
Solve the Test Item
(n – 2)180 = (7 – 2)180 Replace n with 7.
= 5 ● 180 Simplify.
= 900 Multiply.
The sum of the measures of the interior angles of a heptagon is 900°.
Answer: The answer is 900°
Example 2

10. A B C D What is the sum of the interior angles of an octagon? A. 540°
Example 2 CYP

11. (n – 2)180 = (8 – 2)180 Replace n with 8. = 6(180) or 1080 Simplify.
Measure of One Interior Angle
TRAFFIC SIGNS A stop sign is a regular octagon. What is the measure of one interior angle in a stop sign?
Step 1 Find the sum of the measures of the angles. An octagon has 8 sides. Therefore, n = 8.
(n – 2)180 = (8 – 2)180 Replace n with 8.
= 6(180) or 1080 Simplify.
The sum of the measures of the interior angles is 1080°.
Example 3

12. Step 2 Divide the sum by 8 to find the measure of one angle.
Measure of One Interior Angle
Step 2 Divide the sum by 8 to find the measure of one angle.
1080 ÷ 8 = 135
Answer: So, the measure of one interior angle in a stop sign is 135°.
Example 3

13. PICNIC TABLE A picnic table in the park is a regular hexagon
PICNIC TABLE A picnic table in the park is a regular hexagon. What is the measure of one interior angle in the picnic table?
A. 720°
B °
C. 120°
D. 108° A B C D
Example 3 CYP

14. End of the Lesson