The sum of interior and exterior angles of a regular polygon is always 180 degrees.
Let the measure of the interior angle be x and the exterior angle be y.
Given that the ratio of interior angle to exterior angle is 3 and 2, we have the equations:
x/y = 3/2
x = 3y/2
From the sum of interior and exterior angles, we have:
x + y = 180
3y/2 + y = 180
5y/2 = 180
y = 360/5
y = 72
Then we can find the number of sides of the polygon by finding the number of times the exterior angle fits into a full circle (360 degrees):
Number of sides = 360/72
Number of sides = 5
Therefore, the given regular polygon has 5 sides.
Ina given regular polygon the ratio of the interior angle to the exterior angle is 3and 2 how many sides has the polygon
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