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

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Splash Screen

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**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

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**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

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**Polygon Names Side Number Name 3 Triangle 4 Quadrilateral 5 Pentagon 6**

Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon n n-gon

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**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

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**A B C D Classify the polygon. A. pentagon B. hexagon C. heptagon**

D. octagon A B C D Example 1

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Concept

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**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

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**A B C D What is the sum of the interior angles of an octagon? A. 540°**

Example 2 CYP

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**(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

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**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

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**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

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End of the Lesson

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Chapter 6 Quadrilaterals Sec 6.1 Polygons. Polygon 1.Is a plane figure that is formed by 3 or more segments. No two sides with common endpoint are collinear.

Chapter 6 Quadrilaterals Sec 6.1 Polygons. Polygon 1.Is a plane figure that is formed by 3 or more segments. No two sides with common endpoint are collinear.

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