Question

the difference between any two consecutive interior angles of a polygon is 5°.if the smallest angle is 120°. find the number of the sides of the polygon.​

Answer 1

Answer:

According to the given data the angles are in Arithmetic progression

Let 'a'  be the smallest angle of the polygon, 'n' be the number of sides of polygon

and common difference be 'd'

Step-by-step explanation:

According to given data

a=120 ; d=5 ; n=?

Sum of n terms=$\frac{n}{2}$(2a+(n-1)d)

Sum of all angles in a polygon = (n-2)180

therefore;

$\frac{n}{2}$(240+5n-5)=(n-2)180

$\frac{n}{2}$(235+5n)=(n-2)180

$235n +5n^{2} =360n-720$

$5n^{2} -125n+720=0$

$n^{2} -25n+144$=0

therefore;

$n\neq 16$ ; n=9

n is not  equal to 16 because 16 sided polygon does not has 120 as smallest angle

therefore the given polygon is nonagon

Answer 2

hope it helps you ✌