Question

Find the number of sides of a regular polygon in which each interior angle is 162º.
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Answer 1

Answer:

20

Step-by-step explanation:

Sum of the exterior angles of a polygon is 360°

Interior angle + Exterior angle = 180°

⇒ 162° + Exterior angle = 180°

⇒ Exterior angle = 180° - 162° = 18°

⇒ Exterior angle of the regular polygon is 18°

n = Sum of the exterior angles of a polygon / Exterior angle

  =  360° / Exterior angle

⇒ n = 360° / 18° is the number of sides (Let the number of sides be n)

⇒ n = 20

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Answer 2

$\huge\sf\underline\red{Answer}$

THE MEASURE OF EACH INTERIOR ANGLE OF A REGULAR POLYGON = 162°

IF EACH INTERIOR ANGLE IS 162°

THEN EACH EXTERIOR ANGLE IS 18°

SUM OF EXTERIOR ANGLES =360°

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$18n = 360 \\ \\ n = \frac{360}{18} \\ \\ n = 20$

$\bf\underbrace\green{The\:polygon\:has\:20\:sides}$

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