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Question
Each interior angle of a regular polygon is 162°. Another regular polygon has number of sides double the first polygon. Find each interior angle of the second polygon.
Solution
For the given polygon:
Each interior angle = 162°
⇒ Each exterior angle
= 180° - 162°
= 18°
∴ Number of sides in it
= `(360°)/(18)`
= 20
For the other polygon:
Number of sides
= 2 x 20
= 40
∴ Each ecterior anle
= `(360°)/(40)`
= 9°
And, each interior angle
= 180° - 9°
= 171°.
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