Regular Polygons Lesson 7.4: Recognize regular polygons.

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Presentation transcript:

Regular Polygons Lesson 7.4: Recognize regular polygons. Use formulas to find measure of an exterior angle of an equiangular polygon.

Define regular polygon…

Regular Polygons: Equilateral and equiangular

Theorem 58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula E = 360 n

m1 = 360 5 m1 = 72 Find m1 in the figure below Theorem 58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula E = 360 n

Problem #1: 1. How many degrees in each exterior  of an equiangular heptagon? E = 360 7 = 51 3/7

Problem #2: 2. If the exterior angle of a polygon is 18, how many sides does the polygon have? E = 360 n 18 = 360 Plug in 18 for E n 18n = 360 Multiply both sides by n n = 20 sides Divide by 18

First find the exterior angle. Problem #3: 3. If each angle of a polygon is 108, how many sides does it have? First find the exterior angle. 180º - 108º = 72º Set up with correct formula: E = 360 72n = 360 n = 5 The polygon has 5 sides. n

Problem #4: 4. Given the stop sign shown, is NTE scalene, isosceles, equilateral or undetermined? O I T Isosceles N S Q U E