KnowledgeBoat Logo
|

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:

  1. 4

  2. 5

  3. 6

  4. 8

Geometrical Shapes

10 Likes

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) = 360°90°\dfrac{360°}{90°}

⇒ (2n - 4) = 4

⇒ 2n = 4 + 4

⇒ 2n = 8

⇒ n = 82\dfrac{8}{2}

⇒ n = 4

Hence, option 1 is the correct option.

Answered By

3 Likes


Related Questions