Find the number of sides of a regular polygon if each exterior angle is equal to one-third of its adjacent interior angle.

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answer is C.

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Detailed Solution

Concept- Here, we make advantage of the idea that a neighboring internal angle and an outside angle are complementary to one another. We then create an equation by treating the angles as two distinct variables. Form another equation utilizing the relationship stated in the statement. To determine the values of the angles, solve both equations. Utilize the exterior angle formula to get the polygon's number of sides.
The external angle in any polygon is the angle that is outside the polygon but on a line that extends from the polygon. Additionally, the term "adjacent interior angle" refers to the interior angle that lies directly next to the outer angle. As a result, we can conclude that the adjacent inner angle and the outside angle are supplementary because they both lie on the same straight line.
Let's say that the adjacent interior angle is y and that the external angle is x.
Because x and y are complementary,

The declaration that each exterior angle is equal to its adjacent interior angle is now provided to us. So every x is equal to 1/3 of y.
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Substituting the equation 2 in 1
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Substituting the value of x in equation 2
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Now, we apply the exterior angle formula, which is determined by the number of sides in a polygon.
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Hence, the correct answer is option 3.

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