Question

Find the measure of z

144
120
135
108

Answer 1

The sum of interior angles in a regular octagon equals 1080 degrees.

So 1080 / 8 = 135

z = 135

Answer 2

m∠z = 135°

Explanation:

The given figure is a regular octagon. It has 8 sides which are equal in measure. Since it is a regular octagon each interior angle is also in the same measure.

We have formula to find the sum of the interior angles of a polygon.

The sum of the interior angles of a polygon = (n -2)180°, where "n" is the number of sides.

Here n = 8

Now plug in n = 8 and find the sum of the interior angles.

= (8 -2)180

= 6*180

The sum of the interior angles of the regular Octagon = 1080°

Therefore, m∠z =
`(1080)/(8)` = 135°