Question

THE NUMBER OF SIDES IN A REGULAR POLYGON IS 15, THEN FIND THE MEASURE OF EACH EXTERIOR ANGLE.
OPTIONS
a) 20°
b) 24°
c) 36°
d) 18°
who will answer first they will get brainalist if it is correct

Answer 1

The sum of all exterior angles of a polygon equals 360 degrees. Therefore if a regular polygon has exterior angles of 15 degrees then the number of sides must be 360/15 = 24.

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Answer 2

The measure of each exterior angle is 24°

Given :

The number of sides in a regular polygon is 15.

To find :

The measure of each exterior angle is

a) 20°

b) 24°

c) 36°

d) 18°

Solution :

Step 1 of 2 :

Write down the sum of exterior angles

The sum of exterior angles = 360°

Step 2 of 2 :

Calculate the measure of each exterior angle

The number of sides in the regular polygon is 15.

The measure of each exterior angle

$\displaystyle \sf{ = \frac{Sum \:of \:exterior\: angles }{Number\: of \:sides } }$

$\displaystyle \sf{ = \frac{ {360}^{ \circ} }{15} }$

$\displaystyle \sf{ = {24}^{ \circ} }$

Hence the correct option is b) 24°

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