Question

Angles of polygon are in the arithmetic sequence 120,125,130,...........calculate number of sides of the polygon

Answer 1

Answer:

n = 9 or 16

Step-by-step explanation:

The angles are in Arithmetic Progression with common difference 5° and the first angle is 120°

Therefore, sum of n angles = $\frac{n}{2} [2a + (n-1)d]$

$=>\frac{n}{2} [2*120+(n-1)5]$ ---> 1

The sum of interior angles of a polygon= (n-2)180 -----> 2

Equating 1 and 2

$240n + 5(n^2) - 5n = 360n - 720\\=>5(n^2)  - 125n + 720 = 0\\=>(n^2)  - 25n + 144 = 0\\=>n=9\\or,n=16$