Question

If the sum of interior angles of a polygon is thrice the sum of its exterior angles, the number of sides is


ⒼⒾⓋⒺ ⒶⓃⓈⓌⒺⓇ

​

Answer 1

Step-by-step explanation:

Sum of interior angles = 3 x Sum of exterior angles Let exterior angle = x The interior angle = 3x x + 3x=180° => 4x = 180° => x = 180/4 => x = 45° Number of sides = 360/45 = 8

hope it helps

Answer 2

Step-by-step explanation:

Given :-

The sum of interior angles of a polygon is thrice the sum of its exterior angles.

To find :-

Find the number of sides in the polygon ?

Solution :-

We know that

Sum of the interior angles of a polygon of n sides is (n-2)×180°

Sum of the exterior angles of a polygon of n sides is 360°

According to the given problem

The sum of interior angles of a polygon is thrice the sum of its exterior angles.

=> (n-2)×180° = 3×360°

=> n-2 = 3×360°/180°

=> n-2 = 3×2

=>n-2 = 6

=> n = 6+2

=> n = 8

Therefore, n = 8

Answer :-

The number of sides in the polygon is 8

Check:-

If n = 8 then ,

The sum of the interior angles of a polygon of n sides is (n-2)×180°

=> (8-2)×180°

=> 6×180°

=> 1080°

The thrice of Sum of the exterior angles of a polygon of n sides is 360°

=> 360°×3

=> 1080°

Both are equal.

Verified the given relations in the given problem.

Used formulae:-

→ The sum of the interior angles of a polygon of n sides is (n-2)×180°

→ The sum of the exterior angles of a polygon of n sides is 360°

• n = number of sides

Note :-

If the number of sides is 8 then it is an Octagon