A regular polygon has an interior angle measure of 162°. How many sides does this polygon have?

Question

hero · Answer

To find how many sides the polygon has, perform the following steps:

hero · Answer

Subtract 180 - 162 to find the measure of the exterior angle.

hero · Answer

Then take 360 and divide it by the measure of the exterior angle.

anonymous · Answer

so 20?

hero · Answer

Correct.

anonymous · Answer

yay i can maths (it was on purpose)

hero · Answer

And try not to get interior and exterior angles confused.

hero · Answer

There's only two formulas you need to solve problems like this:

If you have a regular polygon, then let i be measure of interior angle, let e be measure of interior angle and n be number of sides of the polygon. Then

i + e = 180
360/e = n

In other words, if you're given the measure of the interior angle, then you can find the number of sides of a polygon using the two formulas above. Use the first formula to find the measure of the exterior angle and the second formula to find the number of sides of the regular polygon.

anonymous · Answer

oh  okay thank you @hero