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.
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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
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