Q. 274.1( 12 Votes )

# 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.

Smallest Angle = 120°

Difference between any two consecutive interior angles of a polygon = 5°

The angles of the polygon will form an A.P. with common difference d as 5° and first term a as 120°.

We know, sum of all angles of a polygon with n sides = 180° (n – 2)

Sn = 180° (n – 2)

Equating both we get

n (240 + 5n – 5) = 360n – 720

5n2 + 240n – 5n – 360n + 720 = 0

5n2 - 125n + 720 = 0

n2 – 25n + 144 = 0

n2 – 16n – 9n + 144 = 0

n (n – 16) – 9 (n – 16) = 0

(n – 9) (n – 16) = 0

n = 9 or 16

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Check Your progress Part 3| Interactive Quiz: Sequence & Series46 mins
Sequence & Series (Lecture 8)35 mins
Use of sigma in finding sum42 mins
Sequence & Series (Lecture 6)42 mins
Sum of Different Kind of Series (Sequence & Series)56 mins
Sequence & Series (Lecture 2)46 mins
Check Your progress Part 1| Interactive Quiz: Sequence & Series46 mins
Sequence & Series (Lecture 3)44 mins
Understand AM, HM & GM - Get JEE Ready57 mins
Quick Recap lecture of Sequence & Series56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses