Question

the vertical angles of a convex polygon are in ap if the smallest angle is 100 and greatest angle is 170. find the number of sides it has.​

Answer 1

Answer:

n= 8, so polygon is octagon.

Step-by-step explanation:

Given:

smallest angle = 100

greatest angle = 170.

as all the angles are in A.P, sum of all the angles = n/2 (a+l)

where n is number of angles , which is equal to number of sides.

a is smallest angle i.e first element in ap

l is largest angle i.e last element in ap

As it is a convex polygon, sum of all angles = (n-2) X 180

where n is number of sides.

equate both equations,

n/2( 100+170) = (n-2) x180

n/2 ( 270) = (n-2) x180

n(135) = 180n - 360

360 = 180n- 135n

45n = 360

n = 360/45

n = 8