Question

if exterior and interior angles of a polygon are in the ratio 1:5 then number of sides of polygon is.
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Answer 1

Answer:

12 sides.

Step-by-step explanation:

Let the angles be 1x and 5x.

In a polynomial, the sum of two angles is 180°.

=> 1x + 5x = 180°

=> 6x = 180°

=> x = 180°/6

=> x = 30°

Measure of angles:

> Exterior angle (1x) = 30°

> Interior angle (5x) = 150°

In a polynomial, the sum of exterior angles is 360°.

> Number of sides × exterior angle = 360°

> 360°/Each exterior angle

=> 360°/30°

=> 12 sides