Each interior angle of a regular polygon is 108°. How many sides has it?
Question 1 Report
Each interior angle of a regular polygon is 108°. How many sides has it?
Answer Details
To find the number of sides of a regular polygon with interior angle 108°, we need to use the formula for the sum of interior angles of a polygon, which is (n-2) x 180°, where n is the number of sides.
Since the polygon is regular, all its interior angles are equal, so we can use the fact that the sum of the interior angles of a polygon is also equal to the number of sides times the interior angle. Therefore, we have:
(n-2) x 180° = n x 108°
Simplifying this equation, we get:
180n - 360 = 108n
72n = 360
n = 5
Therefore, the regular polygon has 5 sides, and the answer is option A.
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