# High School Math : Other Polygons

## Example Questions

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### Example Question #7 : How To Find An Angle In A Polygon

What is the measure of one interior angle of a regular twenty-three-sided polygon (nearest tenth of a degree)?

Explanation:

The measure of each interior angle of a regular polygon with  sides is . We can substitute  to obtain the angle measure:

### Example Question #8 : How To Find An Angle In A Polygon

A regular polygon has interior angles which measure  each. How many sides does the polygon have?

Explanation:

The easiest way to answer this is to note that, since an interior angle and an exterior angle form a linear pair - and thus, a supplementary pair - each exterior angle would have measure . Since 360 divided by the number of sides of a regular polygon is equal to the measure of one of its exterior angles, we are seeking  such that

Solve for :

The polygon has 20 sides.

### Example Question #1 : How To Find The Length Of A Side Of A Polygon

If the area of a regular octagon is 160 and the apothem is 8, what is the side length?

Explanation:

To find the side length from the area of an octagon and the apothem we must use the area of a polygon which is

First plug in our numbers for area and the apothem to get

Then multiply to get

Then divide both sides by 4 to get the perimeter of the figure.

When we have the perimeter of a regular polygon, to find the side length we must divide by the number of sides of the polygon, in this case 8.

After dividing we find the side length is

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