Question

1. What is the sum of the measures of the interior angles of an octagon?.

2. What is the sum of the measures of the interior angles of a 25-gon?
3. What is the measure of each interior angle of a regular hexagon?.
4. What is the measure of each interior angle of a regular 16-gon?
5. What is the sum of the measures of the exterior angles of a decagon?
6. What is the measure of each exterior angle of a regular 30-gon?.
7. If the exterior angle of a regular polygon is 22.5°, how many sides does it have?
8. If the interior angle of a regular polygon measures 170°, how many sides does it have?

Answer 1

1. The sum of the measures of the interior angles of an octagon is 1080

2. The sum of the measures of the interior angles of a 25-gon is 4140°

3. The measure of each interior angle of a regular hexagon is 120°

4. The measure of each interior angle of a regular 16-gon is 157.5°

5. 360°...

6. The measure of each exterior angle of a regular 30-gon is 12°

7. If the exterior angle of a regular polygon is 22.5°,there are 16 sides

8. If the interior angle of a regular polygon measures 170°,it has 36 sides

Explanation:

To find the sum of the measure of interior angles. I used the formula: sum of interior angle= (sides-2)·180°

For finding the interior angle of a polygon, you take the sum of interior angles and divide it by the number of sides.

To find the measure of exterior angles of a polygon .I used the formula: sides= 360°/exterior angle, or exterior angle = 360°/ sides

To find number of sides with the interior angle of a polygon you can use the formula: sides= 360°/180°- interior angle

Hope this helps!