Q140 of 160 Page 144

The ration between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon.

Given, the ratio between exterior angle and interior angle is

1:2.


Let, exterior angle = x


And, interior angle = 5x


Sum of exterior and interior angle is equal to 180.


Hence, x + 5x = 180


6x = 180


x = 30


⟹Total measure of all the exterior angle = 360


⟹Measure of each exterior angle = 30


Therefore, the number of all exterior angles


Hence, the polygon has 12 sides.


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