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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Presentation transcript:

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

Splash Screen

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

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

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

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

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

Concept

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

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

(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

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

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. 128.57° C. 120° D. 108° A B C D Example 3 CYP

End of the Lesson