Question

Find the measure of interior angle C of hexagon OCEANS in which the

Answer 1

Answer:

The measure of the interior angle C is $108^{o}$.

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

                                     = $720^{o}$

Sum of angles in a hexagon = $720^{o}$

⇒ 3x + 15 + 2x + 30 + 5x + 10 + 2x + 55 + 2x + 60 + x - 35 = $720^{o}$

15x + 135 = $720^{o}$

15x = $720^{o}$ - 135

15x = 585

x = $\frac{585}{15}$

  = $39^{o}$

But,

C = 2x + 30

   = 2(39) + 30

   = 78 + 30

   = $108^{o}$

The measure of the interior angle C is $108^{o}$.