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Question

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.


Solution

Let n be the number of sides of a polygon.Let x and 5x be the exterior and interior angles.Since the sum of an interior and the corresponding exterior angle is 180°, we have:x+5x=180°6x=180°x=30°The polygon has n sides. So, sum of all the exterior angles=30n°We know that the sum of all the exterior angles of a polygon is 360°.i.e., 30n=360 n=12

Mathematics
RD Sharma (2019, 2020)
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