Question

2b) Determine the measure of each angle in the regular polygon

Answer 1

Answer: 150

Explanation:

The polygon has 12 equal sides.

formula for :

each angle =
`((n-2)180)/(n)` where n = number of sides = 12

each angle =
`((12-2)180)/(12)`

each angle =
`(10(180))/(12)`

each angle =
`(1800)/(12)`

each angle = 150

Answer 2

Therefore, each angle in the regular polygon has a measure of 135 degrees.

Explanation:

Since the polygon is regular, all angles are congruent. Let's call the measure of each angle x.

The sum of the interior angles of a polygon with n sides is given by the formula (n-2) x 180 degrees.

In this case, the polygon has 8 sides, so:

(8-2) x 180 = 6 x 180 = 1080 degrees

The sum of the interior angles is 1080 degrees.

Since all angles are congruent, we can divide the sum by the number of angles to find the measure of each angle:

x = 1080 / 8 = 135 degrees