Question

A regular polygon is shown, with one of its angle measures labeled a. 9 sided regular polygon with one angle labeled a If m∠a = (8z + 52)°, find the value of z. z = 128 z = 48 z = 16 z = 11

Answer 1

The value of z is 11.

Explanation:

To find the value of z, we can equate the angle measure to the given expression and solve for z.

m∠a = (8z + 52)°

Since we know that the polygon is a regular polygon with 9 sides, all of its angles are equal. In a regular polygon with n sides, the formula to calculate the measure of each angle is:

m∠a = (n - 2) * 180 / n

For a 9-sided polygon, this becomes:

m∠a = (9 - 2) * 180 / 9

m∠a = 7 * 180 / 9

m∠a = 140°

Setting the expression for m∠a equal to 140°, we have:

8z + 52 = 140

Now we can solve for z:

8z = 140 - 52

8z = 88

z = 88 / 8

z = 11

Therefore, the value of z is 11.