2. Main Idea and New Vocabulary Example 1: Classify Polygons
Key Concept: Interior Angle Sum of a Polygon
Example 2: Sum of Interior Angle Measures
Example 3: Real-World Example
Lesson Menu

3. Find the sum of the angle measures of a polygon and the measure of an interior angle of a regular polygon.
polygon
interior angle
equiangular
regular polygon
Main Idea/Vocabulary

4. Answer: It is not a polygon because it has a curved side.
Classify Polygons
Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why.
Answer: It is not a polygon because it has a curved side.
Example 1

5. D. No; the segments do not intersect at their endpoints.
Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why.
A. yes; pentagon
B. yes; hexagon
C. yes; heptagon
D. No; the segments do not intersect at their endpoints.
Example 1 CYP

6. Key Concept 3

7. Sum of Interior Angle Measures
ALGEBRA Find the sum of the measures of the interior angles of a 13-gon.
S = (n – 2)180 Write an equation.
S = (13 – 2)180 A 13-gon has 13 sides. Replace n with 13.
S = (11)180 or 1,980 Simplify.
Answer: The sum of the measures of the interior angles of a 13-gon is 1,980°.
Example 2

8. ALGEBRA Find the sum of the measures of the interior angles of an 18-gon.
C. 3,060°
D. 3,240°
Example 2 CYP

9. DESIGN A designer is creating a new logo for a bank
DESIGN 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.
Example 3

10. Step 1 Find the sum of the measures of the angles.
S = (n – 2)180 Write an equation.
S = (5 – 2)180 Replace n with 6.
S = (3)180 or 540 Simplify.
The sum of the measures of the interior angles is 540°.
Example 3

11. Step 2 Divide 540 by 5, the number of interior angles, to find the measure of one interior angle.
540 ÷ 5 = 108
Answer: The measure of one interior angle of a regular pentagon is 108°.
Example 3

12. ART An artist is creating a sculpture that is made up of regular decagons. Find the measure of an interior angle of a regular decagon.
A. 144°
B. 225°
C. 1,440°
D. 1,800°
Example 3 CYP