Question

each interior angle of a n sided regular polygon is 162 degrees. find the interior angle of another polygon with 2n sides

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Answer 1

it has mentioned that a polygon has interior angles of 162o. It is assumed from this that all interior angles are 162o.

As interior angles are 162o, each exterior angle is 180o−162o=18o.

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

Number of angles / sides of polygon are 360o18o=20
so another polygon has sides = 2 × 20 = 40
sides
Interior Angle = 180° - 360°/n 
Interior Angle = 180 - 360/40
Interior Angle = 180 - 9
Interior Angle = 171° 

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