Question

PLEASE ANSWER, I am so confused!! Number 12, 13, and 14. I would really appreciate it is you help, step by step.

Answer 1

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

If a polygon is regular, than all angles are congruent.
The polygon has n sides and n angles, so each angle measures
[(n - 2)180]/n

In problems 12, 13, and 14, you are given the measure of one angle of a regular polygon.
Set the measure equal to the formula above, and solve for n, the number of sides.

12.


`((n - 2)180)/(n) = 120`


`(n - 2)180 = 120n`


`180n - 360 = 120n`


`60n = 360`


`n = 6`

Answer: 6 sides

13.


`((n - 2)180)/(n) = 108`


`(n - 2)180 = 108n`


`180n - 360 = 108n`


`72n = 360`


`n = 5`

Answer: 5 sides

14.


`((n - 2)180)/(n) = 135`


`(n - 2)180 = 135n`


`180n - 360 = 135n`


`45n = 360`


`n = 8`

Answer: 8 sides