Answer:
The size of each of the three equal unknown angles is [tex]120^{0}[/tex].
Explanation:
Let the the unknown angle be represented by x. The polygon is a hexagon, which has three sides and angles.
sum of angle in the hexagon = (n - 2) x [tex]180^{0}[/tex]
n = 6, so that;
Sum of angle in the hexagon = ( 6 - 2) x [tex]180^{0}[/tex]
= 4 x [tex]180^{0}[/tex]
= [tex]720^{0}[/tex]
Therefore;
x + x + x + [tex]145^{0}[/tex] + [tex]100^{0}[/tex] + [tex]115^{0}[/tex] = [tex]720^{0}[/tex]
3x + [tex]360^{0}[/tex] = [tex]720^{0}[/tex]
3x = [tex]720^{0}[/tex] - [tex]360^{0}[/tex]
3x = [tex]360^{0}[/tex]
x = [tex]120^{0}[/tex]
The size of each of the three equal unknown angles is [tex]120^{0}[/tex].
