If the individual measure of an angle in a regular polygon is 156° how many sides does the polygon have?

2 Answers
Jun 8, 2018

15

Explanation:

The sum of the internal angles of a polygon with n sides is (n-2) * 180 degrees.

If the polygon is regular, all the angles have the same measure, which means that each angle is

\frac{(n-2) * 180}{n} degrees.

We know that this equals 156, so we have

\frac{(n-2) * 180}{n} = 156

Multiply both sides by n:

(n-2) * 180 = 180n - 360= 156n

Subtract 156n from and add 360 to both sides

180n-156n = 24n= 360

Divide both sides by 24:

n = \frac{360}{24} = 15

Jun 8, 2018

15 sides

Explanation:

The sum of the exterior angles of any polygon is always 360°.

You can calculate the number of sides from (360°)/("ext angle")

Ext angle = 180°-156° = 24°

360/24 = 15 sides