tybogie2003
Answered

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Find the measure of interior angle C of hexagon OCEANS in which the
measure of the interior angles are:
O: 3x + 15, C: 2x + 30, E: 5x + 10, A: 2x + 55, N: 2x + 60, and S: x - 35.

Sagot :

olayemiolakunle65

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].

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