in a regular polygon, each interior angle is twice the exterior angle.

1.	in a regular polygon, each interior angle is twice the exterior angle. the number of sides of the polygon is _________
Answer» Answer: 8 or OCTAGON Step-by-step explanation: Concept : Sum of Interior angle + Sum of Exterior angle = 180° Let the interior angle be 'x' *=> Exterior angle = 3 Interior angle = 3 x => x + 3x = 180° => 4x = 180° => x = 180 / 4 => x = 45° We also know that, Exterior angle = 360° / n Where n represents the number of sides of a polygon. => n = 360° / Exterior angle => n = 360° / 45° => n = 8 Hence it is a 8 sided polygon which is an octagon.**

in a regular polygon, each interior angle is twice the exterior angle. the number of sides of the polygon is _________

Answer»

Answer:

Step-by-step explanation:

Concept : Sum of Interior angle + Sum of Exterior angle = 180°

Let the interior angle be 'x'

=> Exterior angle = 3 * Interior angle = 3 x

=> x + 3x = 180°

=> 4x = 180°

=> x = 180 / 4

=> x = 45°

We also know that,

Exterior angle = 360° / n

Where n represents the number of sides of a polygon.

=> n = 360° / Exterior angle

=> n = 360° / 45°

=> n = 8

Hence it is a 8 sided polygon which is an octagon.