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Lesson Menu Five-Minute Check (over Lesson 11–4) Then/Now New Vocabulary Example 1: Classify Polygons Key Concept: Interior Angles of a Polygon Example 2: Standardized Test Example Example 3: Real-World Example: Measure of One Interior Angle Example 4: Find Tessellations

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Over Lesson 11–4 5-Minute Check 1 A.128 B.126 C.124 D.122 Find the value of x.

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

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Over Lesson 11–4 5-Minute Check 3 A.cube B.parallelogram C.rhombus D.quadrilateral Classify the quadrilateral.

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Over Lesson 11–4 5-Minute Check 4 A.square B.parallelogram C.rhombus D.quadrilateral Classify the quadrilateral.

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Over Lesson 11–4 5-Minute Check 5 A.a parallelogram with exactly one pair of parallel sides B.a quadrilateral with exactly one pair of parallel sides C.a parallelogram with at least two congruent sides D.a quadrilateral with at least two congruent sides Which statement best describes a trapezoid?

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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 tessellation

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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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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. A. 1260° B. 1080° C. 900° D. 1620° 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.

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Example 2 Answer: The answer is C. 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°.

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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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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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Example 4 Find Tessellations Determine whether or not a tessellation can be created using only regular decagons. If not, explain. The measure of each interior angle of a regular decagon is 144°. The sum of the measures of the angles where the vertices meet must be 360°. So, solve 144°n = 360. 144n= 360Write the equation. Divide each side by 144.

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Example 4 Find Tessellations Answer: Since 360 is not evenly divisible by 144, it cannot be used to make a tessellation. n= 2.5Simplify.

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Example 4 CYP A.hexagon B.pentagon C.quadrilateral D.triangle Which regular polygon cannot be used to create a tessellation?

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End of the Lesson

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