Question

-15 POINTS-
How many sides does a regular polygon have if one interior angle measures 144°

Answer 1

Answer: 10 sides

Explanation:

You can always use the given formula to calculate but I (personally) find it much easier to calculate the number of sides using the exterior angle.

To calculate the exterior angle, it is 180 - the interior angle.

In this example, the exterior angle would be 180-144 = 36°

Because it is a regular polygon, we know that all the angles in the shape are the same.

In all polygons, the exterior angles always add up to 360 degrees.

So divide 360 by 36 (the size of each exterior angle), and you get 10.

360/36 = 10

Answer 2

Number of sides in the given regular polygon will be 10.

To find the number of sides n a regular polygon has given that one interior angle measures 144°, we use the formula for the measure of each interior angle in a regular polygon:

`\[((n - 2) * 180)/(n) = \text{measure of one interior angle}\]`

When we plug 144° into the formula and solve for n , we find that n = 10 . Therefore, a regular polygon with one interior angle measuring 144° has 10 sides.