MATH SOLVE

3 months ago

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

Accepted Solution

A:

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.

[tex] \dfrac{(n - 2)180}{n} = 120 [/tex]

[tex] (n - 2)180 = 120n [/tex]

[tex] 180n - 360 = 120n [/tex]

[tex] 60n = 360 [/tex]

[tex] n = 6 [/tex]

Answer: 6 sides

13.

[tex] \dfrac{(n - 2)180}{n} = 108 [/tex]

[tex] (n - 2)180 = 108n [/tex]

[tex] 180n - 360 = 108n [/tex]

[tex] 72n = 360 [/tex]

[tex] n = 5 [/tex]

Answer: 5 sides

14.

[tex] \dfrac{(n - 2)180}{n} = 135 [/tex]

[tex] (n - 2)180 = 135n [/tex]

[tex] 180n - 360 = 135n [/tex]

[tex] 45n = 360 [/tex]

[tex] n = 8 [/tex]

Answer: 8 sides

(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.

[tex] \dfrac{(n - 2)180}{n} = 120 [/tex]

[tex] (n - 2)180 = 120n [/tex]

[tex] 180n - 360 = 120n [/tex]

[tex] 60n = 360 [/tex]

[tex] n = 6 [/tex]

Answer: 6 sides

13.

[tex] \dfrac{(n - 2)180}{n} = 108 [/tex]

[tex] (n - 2)180 = 108n [/tex]

[tex] 180n - 360 = 108n [/tex]

[tex] 72n = 360 [/tex]

[tex] n = 5 [/tex]

Answer: 5 sides

14.

[tex] \dfrac{(n - 2)180}{n} = 135 [/tex]

[tex] (n - 2)180 = 135n [/tex]

[tex] 180n - 360 = 135n [/tex]

[tex] 45n = 360 [/tex]

[tex] n = 8 [/tex]

Answer: 8 sides