Question

in a regular polygon each interior angle is thrice the exterior angle the number of side of the polygon is​

Answer 1

Answer:

Step-by-step explanation:Hey there !

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.

Hope my answer helped !

Answer 2

$\huge \star \mathtt \pink{ \underline{Answer}} \star$

✯Let the Exterior angle be a

• Interior angle = 3a

✯We know that,

• Exterior angle + Interior angle = 180

=> a + 3a = 180

=> 4a = 180

=> a = 45°

• Interior angle = 3 × 45 = 135°

• Exterior angle = 45°

✯Now,

• n × Each Exterior angle = 360

=> n × 45 = 360

=> n = 8

Number of sides = 8