Question

a regular polygon, the inner angle is 3 times of its outer angle. what is the measurement of an inner angle​

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MATHS

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon

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ANSWER

The sum of interior angles of a regular polygon is three the sum of its exterior angles.

Sum of all interior angles of a regular polygon = 180

o

(n−2) where n = number of sides of polygon

Sum of all exterior angle of a regular polygon = 360

o

According to question,

180

o

(n−2)=3×360

o

=>(n−2)=6

=>n=8

Number of sides of the polygon = 8