Question

50 points!

Determine the degree measure of one angle of a 24-sided regular polygon.

a. 165°
b. 180°
c. 3,960°
d. 4,320°

Answer 1

Answer: The answer is 165

Explanation:

The number of triangles is 2 less than the number of sides.

The number of triangles multiplied by 180 equals the sum of the interior angles. This makes sense because each triangle has an angle sum of 180.

24-2 equals 22 times 180 equals 3,960 but were trying to find one angle so you would do 3,960 divided by 24 to get 165.

I also got it right on my test if you needed more conformation:)

Answer 2

• a. 165°

Explanation:

Sum of interior angles of n-sided polygon is:

• Sₙ = 180°(n - 2)

Substitute n with 24:

• S₂₄ = 180°(24 - 2) = 180°(22) = 3960°

Find measure of one interior angle:

• 3960°/24 = 165°

Correct choice is a.