Question

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

Answer 1

`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`

Answer 2

`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