Question

Find the number of sides of a regular polygon if each interior angle of the polygon is (a) 140 (b) 162, (c) 172, (d) 175.

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Answer 1

Answer:

a) 140

Let the number of sides in the given regular polygon be n

Since the interior angle of the given regular polygon is 140

The sum of the interior angles = (2n - 4)×

right angle

so,140n = (2n - 4) ×90

or, 140n =180n-360

n = 9 sides

Hence, the number of sides in the given polygon is 9

b) 162

As interior angles are 162 , each exterior angle is 180 - 162 =18°

Sum of all the exterior angles of a polygon is always 360 and as each exterior angle is 18

Number of angles / sides of polygon are

360/10 = 20

c) 172

when interior angle =172° then exterior angle =180–172 =8

number of sides polygon has =360/8 =90 =45 sides

The polygon has 45 sides of equal length

d)175

A regular polygon with each interior angle of 175 deg will have each exterior angle as 180–175 = 5 deg. Hence the number of sides in the regular polygon = 360/5 = 72 sides

Step-by-step explanation:

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