Question

The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides.

40
What is the measure of an interior​ angle?

Answer 1

The measure of an interior angle of the regular polygon is 140 degrees. The regular polygon has 9 sides.

Step-by-step explanation:

The measure of an exterior angle of a regular polygon is equal to 360 divided by the number of sides of the polygon. In this case, the measure of the exterior angle is given as 40 degrees. So we can set up an equation:

• 360/n = 40
• 360 = 40n
• n = 360/40
• n = 9

Therefore, the measure of an interior angle would be 180 - 40 = 140 degrees. Since the measure of an interior angle of a regular polygon can be found using the formula (n-2) * 180, where n represents the number of sides, we can substitute the value of n to calculate the number of sides:

• (n-2) * 180 = (9-2) * 180 = 7 * 180 = 1260

Answer 2

The polygon has 9sides with an interior angle measure of 140°

Step-by-step explanation:

The exterior angle of a regular polygon=360°/n

40°=360°/n

n=360°/40°=9

So the polygon has 9 sides thus, a nonagon.

The measure of the interior angle=(n-2)180°/n

=(9-2)×180°/9=140°