Mathematics
The sum of all interior angles of a regular polygon is equal to sum of all its exterior angles. The number of sides in the polygon is:
4
5
6
8
Geometrical Shapes
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Answer
It is given that the sum of all interior angles of a regular polygon is equal to the sum of all its exterior angles.
According to the properties of a polygon, if there are n sides, then the sum of its interior angles is (2n - 4) x 90° and the sum of its exterior angles is 360°.
⇒ (2n - 4) x 90° = 360°
⇒ (2n - 4) =
⇒ (2n - 4) = 4
⇒ 2n = 4 + 4
⇒ 2n = 8
⇒ n =
⇒ n = 4
Hence, option 1 is the correct option.
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