Question

The interior angles of a polygon are in A.P., the smallest angle is 75° and the common difference is 10°. Find the number of sides of the polygon.

Answer 1

Step-by-step explanation:

Smallest angle=75degree

Common difference=10

A P is 75, 85, 95,……..

The sum of interior angles of a polygon= (n-2)180

Hence Sum of n terms of an A P = (n-2)180

n/2 {2.75+(n-1)10} = 180(n-2)

n/2(150+10n-10) = 180n- 360

n/2(140+10n) -180n+360=0

70n+5n²-180n+360_=0

5n²-110n+360=0

n²-22n+72=0

n(n-22)2(11n+36)

hence number of sides can be

Answer 2

Answer:

solve it furthur...to get the answer