The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is 129°. The greatest measurement is

Rui Baldwin

Rui Baldwin

Answered question

2021-05-16

The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is 129. The greatest measurement is 159. Find the number of sides in this polygon.

Answer & Explanation

joshyoung05M

joshyoung05M

Skilled2021-05-17Added 97 answers

We are given a1=129 (least angle) and an=159 (greatest angle, representing the nnth angle). Since the number of angles is equal to the number of sides in a convex polygon, we need to find n.
Use the formula for finding the sum of the first nn term of an arithmetic sequence:
Sn=n2(a1+a2)
Sn=n2(129+159)
Sn=144n
The sum of the angles of a convex polygon with nn sides (in degrees) is given by: Sn=180(n2)
Equating (1) and (2), we solve for n: 144n=180(n2)
144n=180n360
36n=360
n=10
So, the convex polygon has 10 sides.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

Answer is given below (on video)

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