Question

pls help! will give brainlist!

find each angle measure in the regular polygon

a. 144°
b. 135°
c. 180°
d. 140°

Answer 1

The answer is: A

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144°

Answer 2

Answer: a. 144 degrees

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Work Shown:

E = exterior angle

n = number of sides

For any regular polygon, E = 360/n.

In this case, n = 10 as there are 10 sides, so E = 360/n = 360/10 = 36 degrees is the measure of each exterior angle.

Each interior angle is 180-E = 180-36 = 144 degrees

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An alternative is to plug n = 10 into the formula below to get the measure of each interior angle i

i = 180(n-2)/n

i = 180(10-2)/10

i = 180(8)/10

i = 1440/10

i = 144

note: S = 180(n-2) is the sum of all the interior angles of any convex polygon. Dividing this sum over n will evenly divide the angle total to each interior angle.