Question

the exterior angle of a regular polygon is 1 fifth of its interior angle. How many sides does the polygon have?

Answer 1

Answer:

Step-by-step explanation:

let the interior angle be x

exterior angle will be

(180- x )

(180 - x ) = 1x/5

900-5x = x

900= x + 5x

900= 6x

x = 900/6

x= 150

each interior angle is 150°

the number of sides are

{ n - 2 ) * 180} /n = 150

( n - 2 ) * 180 = 150n

n-2 = 150n / 180

n-2 = 5n/6

6(n - 2)= 5n

6n - 5n = 12

n = 12

number of sides= 12

Answer 2

Answer:

let the interior angle be x

so exterior angle is x/5

x+x/5 = 180°

5x+x/5=180°

6x=180×5

x=180×5/6

x=150°

the number of sides of the regular polygon with interior angle 150∘ is 12.