Answer:
The measure of the interior angle C is [tex]108^{o}[/tex].
Step-by-step explanation:
Sum of angles in a polygon = (n - 2) x 180
where n is the number of sides of the polygon.
For a hexagon, n = 6. So that;
Sum of angles in a hexagon = (6 - 2) x 180
= 4 x 180
= [tex]720^{o}[/tex]
Sum of angles in a hexagon = [tex]720^{o}[/tex]
⇒ 3x + 15 + 2x + 30 + 5x + 10 + 2x + 55 + 2x + 60 + x - 35 = [tex]720^{o}[/tex]
15x + 135 = [tex]720^{o}[/tex]
15x = [tex]720^{o}[/tex] - 135
15x = 585
x = [tex]\frac{585}{15}[/tex]
= [tex]39^{o}[/tex]
But,
C = 2x + 30
= 2(39) + 30
= 78 + 30
= [tex]108^{o}[/tex]
The measure of the interior angle C is [tex]108^{o}[/tex].
