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Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 2 A.80 B.60 C.40 D.20 Find the value of x.

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Splash Screen

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

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Vocabulary polygon diagonal interior angle regular polygon A simple closed figure in a plane formed by three or more line segments 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

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Side NumberName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon 8Octagon 9Nonagon 10Decagon nn-gon

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Example 1 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.

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

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Concept

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Example 2 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)180Replace n with 7. =5 ● 180Simplify. = 900Multiply. The sum of the measures of the interior angles of a heptagon is 900°. Answer: The answer is 900°

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A.A B.B C.C D.D Example 2 CYP A.540° B.720° C.900° D.1080° What is the sum of the interior angles of an octagon?

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Example 3 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 1Find the sum of the measures of the angles. An octagon has 8 sides. Therefore, n = 8. (n – 2)180=(8 – 2)180Replace n with 8. =6(180) or 1080Simplify. The sum of the measures of the interior angles is 1080°.

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

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A.A B.B C.C D.D Example 3 CYP A.720° B.128.57° C.120° D.108° PICNIC TABLE A picnic table in the park is a regular hexagon. What is the measure of one interior angle in the picnic table?

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End of the Lesson

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