Question

find the number of sides of a regular polygon if each interior angle is equal to 170 degree

Answer 1

A regular polygon with each interior angle of 170 deg will have each exterior angle as 180–170 = 10 deg. Hence the number of sides in the regular polygon = 360/10 = 36 sides.

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Answer 2

Given: Each interior angle of a regular polygon is equal to 170 degree.

To find: The number of sides of the regular polygon.

Solution:

• The interior angle of a regular polygon is the angle formed between any two consecutive sides.
• In order to solve the given question, the difference between 180 degree and the interior angle is to be found out first.

        $180 - 170 = 10$

• So, the difference is 10 degree.

• Then, 360 degree is divided by the difference found.

        $\frac{360}{10} = 36$

• The quotient gives the number of sides of the regular polygon.

Therefore, the number of sides of the regular polygon is 36.