Mathematics
Two alternate sides of a regular polygon, when produced, meet at right angle. Calculate the number of sides in the polygon.
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Answer
Let the measure of each exterior angle be x and the number of sides be n. Therefore we can write:
n =
Given that:
⇒ 2x + 90° = 180°
⇒ 2x = 180° - 90°
⇒ 2x = 90°
⇒ x =
⇒ x = 45°
Using x = 45° to find n:
⇒ = 45°
⇒ n =
⇒ n = 8
Hence, the number of sides is 8.
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