Question

A and B are regular polygons and A has two more sides than B. The measure of each interior angle of A is greater than the measure of the interior angle of B. How many sides does A have? Explain how.

A.) 6. B.)8 C.) 10 D.) 12

Answer 1

Answer:

A can have 6, 8, 10 or even 12 sides.

Explanation:

The formula to figure out the measure of interior angles in regular polygons is the following, where n is the number of sides.

$\frac{180*(n-2)}{n}$

For all the options the measure of each interior angle of A is greater than the measure of the interior angle of B when A has two more sides than B.

Answer 2

The sides of Polygon A is 12 (Option A).

What is the proof that the side of Polygon A is 12?

Please note that the Exterior angles differ by 6.

a = b + 2

Recall that the sum of the Interior angles of a polygon is equal to 360°. Hence,

360/b = 360/(b+2) + 6

360/b = (360 + 6b + 12)/(b+2)

360*(b+2) = b*(6b + 372)

360b + 720 = 6b^2 + 372b

b^2 + 2b - 120 = 0

b = 10 Therefore,

Side A = 12 (Option D)

Learn more about Polygons at:

https://brainly.com/question/1487036