Question

Find x using the picture provided.

Answer 1

Given:

Interior angles of a polygon.

7x°, 2x°, 8x°, 60°, 10x°, 8x° and 35°.

To find:

The value of x.

Solution:

Number of sides = 7

Using sum of interior angles of a polygon formula:

`\text{Sum} = (n - 2) * 180^\circ`

`7x^\circ + 2x^\circ + 8x^\circ + 60^\circ + 10x^\circ + 8x^\circ + 35^\circ = (n - 2) * 180^\circ`

Adding like terms.

`35x^\circ + 95^\circ = (n - 2) * 180^\circ`

Substitute n = 7.

`35x^\circ + 95^\circ = (7 - 2) * 180^\circ`

`35x^\circ + 95^\circ =5 * 180^\circ`

`35x^\circ + 95^\circ =900^\circ`

Subtract 95° from both sides.

`35x^\circ + 95^\circ -95^\circ=900^\circ-95^\circ`

`35x^\circ =805^\circ`

Divide by 35° on both sides.

`$(35x^\circ)/(35^\circ) =(805^\circ)/(35^\circ)`

x = 23

The value of x is 23.