Question

1. If the sum of the interior angles of a polygon is 540 degrees, then how many sides does the polygon have?

a. 5
b. 6
c. 7
d. 8

2. What is the measure of one angle in a regular 16-gon?

a. 2,520 degrees
b. 202.5 degrees
c. 157.5 degrees
d. 78.75 degrees

3. The measure of each exterior angle of a regular pentagon is______ the measure of each exterior angle of a regular nonagon.

a. greater than
b. less than
c. equal to

Answer 1

1 is A
2 is 180 - 360/16 = 157.5 or C
3 is A

Answer 2

1)Option A 2)c. 157.5 degrees 3)a. greater than

Explanation:

1)The sum of the measures of the interior angles of a polygon with n sides is

(n – 2)180 where n denotes the number of sides of the polygon.

Given : 540=(n-2)*180

Dividing both sides by 180 we have:

3=n-2

Adding 2 both sides n=5.

Option A.

2) Sum of angles of any polygon = (n-2)*180

If n=16 then sum of angles =(16-2)*180=2,520 degrees

Measure of each angle = 2,520÷16= 157.5 degrees.

Option C.

3) Each exterior angle of pentagon is 72 degrees. Each exterior angle of regular nonagon is 40 degrees.Thus

The measure of each exterior angle of a regular pentagon is__Greater than ____ the measure of each exterior angle of a regular nonagon.

a. greater than