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EXAMPLE 1

It is not a polygon. The bottom edge does not have line segments. a. b. It is a regular polygon. Its angles have equal measures, and its sides have equal lengths. EXAMPLE 1. Identifying Figures. Is the bottom of the box a polygon , a regular polygon , or not a polygon ? Explain.

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EXAMPLE 1

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  1. It is not a polygon. The bottom edge does not have line segments. a. b. It is a regular polygon. Its angles have equal measures, and its sides have equal lengths. EXAMPLE 1 Identifying Figures Is the bottom of the box a polygon, a regular polygon, or not a polygon? Explain.

  2. Find the measure of one angle in a regular octagon. o o (8 – 2) 180 (n – 2) 180 = 8 n o 1080 = 8 o 135 = ANSWER o The measure of one angle in a regular octagon is135. EXAMPLE 2 Finding an Angle Measure SOLUTION A regular octagon has 8 sides, so n = 8. Substitute 8 for n. Simplify numerator. Divide.

  3. ANSWER o The sum of angle measures in a 9-gon is1260 . for Examples 1 and 2 GUIDED PRACTICE 1.Find the sum of the angle measures in a 9-gon.

  4. Find the measure of one angle in a regular heptagon. Round to the nearest tenth of a degree. 2. ANSWER The measure of one angle in a regular heptagon is128.6 . o for Examples 1 and 2 GUIDED PRACTICE

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