Question

(b) Four of the interior angles of a 12 sided polygon are each x °. The other angles are 2xº each. Calculate the value of x.​

Answer 1

x = 90

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 12 , then

sum = 180° × 10 = 1800

There are 12 interior angles

Given 4 are x, then 8 are 2x , so

4x + 8(2x) = 1800

4x + 16x = 1800

20x = 1800 ( divide both sides by 20 )

x = 90

Answer 2

Explanation:

Sum of all the angles of 12 sided polygon= (n -2)*180

= (12 - 2 )*180 = 10 * 180 = 1800

Four interior angle each of xº + 8 interior angles each of 2xº = 1800

4*x + 8*2x = 1800

4x + 16x = 1800

20x = 1800

x = 1800/20

x = 90°