Mathematics Question and Solution
Let x be the single interior angle of the regular polygon.
a = 180-x-20
a = (160-x)°
b = 180-x-30
b = (150-x)°
c = 180(5-2)
c = 540°
d = 2(360-x)°
It implies;.
a+b+d+86 = c
(160-x)+(150-x)+2(360-x)+86 = 540
396+720-4x = 540
1116-540 = 4x
4x = 576
x = 144°
Again, x is the single interior angle of the regular polygon.
Calculating n, number of sides of the regular polygon.
Sum = 180(n-2)
And Sum = xn, where x = 144°
It implies;
144n = 180n-360
180n-144n = 360
36n = 360
n = 10
Therefore, the polygon is a regular decagon.
