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In a regular polygon, the ratio of the inner and outer angle is 7 : 2. What is each angle? How many sides does the polygon |
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Answer» Let the inner angle be 7x and the outer angle 2x . Inner angle + outer angle = 180° 7x + 2x = 180° 9x = 180° x = 180 ÷ 9 = 20° Inner angle = 7x = 7 × 20 = 140° Outer angle = 2x = 2 × 20 = 40° Sum of the outer angles of a polygon of n sides is 360°. Since it is a regular polygon, the outer angles are equal, n × 40 = 360° n = \(\frac{360}{40}\) = 9 Number of sides of the polygon = 9 |
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