Respuesta :
Answer:
Step-by-step 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:
6
Step-by-step 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
