Main Idea and New Vocabulary Example 1: Classify Polygons

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Presentation transcript:

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

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

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

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

Key Concept 3

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

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

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

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

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

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