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 the measure of each exterior angle of a regular nonagon. a. greater than b. less than c. equal to

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

Step-by-step 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

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