Question

The measure of the interior angles taken in order of a polygon from the arithmetic sequence the least measurement in the sequence is 85° the greatest measurement is 215° find the number of sides in the given polygon

Answer 1

Answer:

12

Step-by-step explanation:

ANSWER

Let n denote the number of sides of the polygon.

Now, the measures of interior angles form an arithmetic sequence.

Let the sum of the interior angles of the polygon be

S

n

=a+(a+d)+(a+2d)+....+l, where a=85 and l=215.

We have, S

n

=

2

n

[l+a]...(1)

We know that the sum of the interior angles of a polygon is (n−2)×180

∘

.

Thus, S

n

=(n−2)×180

From (1), we have

2

n

[l+a]=(n−2)×180

⇒

2

n

[215+85]=(n−2)×180

150n=180(n−2)⇒n=12.

Hence, the number of sides of the polygon is 12.