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:
[tex]\text{Sum} = (n - 2) \times 180^\circ[/tex]
[tex]7x^\circ + 2x^\circ + 8x^\circ + 60^\circ + 10x^\circ + 8x^\circ + 35^\circ = (n - 2) \times 180^\circ[/tex]
Adding like terms.
[tex]35x^\circ + 95^\circ = (n - 2) \times 180^\circ[/tex]
Substitute n = 7.
[tex]35x^\circ + 95^\circ = (7 - 2) \times 180^\circ[/tex]
[tex]35x^\circ + 95^\circ =5 \times 180^\circ[/tex]
[tex]35x^\circ + 95^\circ =900^\circ[/tex]
Subtract 95° from both sides.
[tex]35x^\circ + 95^\circ -95^\circ=900^\circ-95^\circ[/tex]
[tex]35x^\circ =805^\circ[/tex]
Divide by 35° on both sides.
[tex]$\frac{35x^\circ}{35^\circ} =\frac{805^\circ}{35^\circ}[/tex]
x = 23
The value of x is 23.
