Question

The least measurement is the sequence is 128. The greatest measurement is 172. Find the number of sides in this polygon given the sum of the measures is equal to 180 (n-2) degrees

Answer 1

the number of sides is 12

Explanation:

The computation of the number of sides in the polygon is shown below:

As we know that

S_n = n ÷ 2 (a_1 + a_n)

= n ÷ 2 × (128 + 172)

= 150 n

Now given that the sum of the measures = 180 (n - 2)

So,

Sn = 180 (n - 2)

150n = 180n - 360

30n = 360

n = 12

Hence, the number of sides is 12