Question

One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?

Answer 1

Explanation:

160+112n=180k

112n=180k-160

for k=1

180-160=20(not divisible by 112)

k=2

180*2-160=360-160=200(not divisible by 112)

k=3

180*3-160=540-160=380(not divisible by 112)

180*4-160=720-160=560(divisible by 112)

so number of sides=560/112 +1=5+1=6

or (n-2)180=720

n-2=720/180=4

n=4+2=6

Answer 2

6

Explanation:

The sum of interior angle of a polygon is (n - 2)180.

But in the convex polygon given in the question, we know that the sum of the interior angles is as follows: : 160 + 112(n - 1)

Equating both will yield the following:

180n -360 = 112n - 112 + 160

180n - 360 = 112n + 48

180n - 112n = 360 + 48

68n = 408

n = 408/68 = 6

Hence , the convex polygon has 6 sides