Question

Find the value of x.

Answer 1

x = 82

Explanation:

The sum of the interior angles of a polygon with n sides = (n-2) x 180°

This polygon has 7 sides so the sum of its interior angles
= (7-2) x 180°

= 5 x 180°

= 900°

Adding up the given angles we get
x + 160 + 2x + 125 + 110 + 112 + 147 = 900

3x + 654 = 900

3x = 900 - 654

3x = 246

x = 246/3 = 82

Answer 2

x = 82

Explanation:

Sum of interior angles of a polygon

`S=(n-2) * 180^(\circ)`

where n is the number of sides.

The given polygon has 7 sides:

• n = 7

To find the value of x, substitute the sum of the interior angles and the found value of n into the formula and solve for x:

`\implies x+160+2x+125+110+112+145=(7-2)* 180`

`\implies x+2x+160+125+110+112+145=5* 180`

`\implies 3x+654=900`

`\implies 3x+654-654=900-654`

`\implies 3x=246`

`\implies (3x)/(3)=(246)/(3)`

`\implies x=82`

Therefore, the value of x is 82.