Given O A ‾ ⊥ O C ‾ OA ⊥ OC start overline, O, A, end overline, \perp, start overline, O, C, end overline m ∠ B O C = 6 x − 6 ∘ m∠BOC=6x−6 ∘ m, angle, B, O, C, equals, 6, x, minus, 6, degrees m ∠ A O B = 5 x + 8 ∘

x = 8

m∠BOC = 37°

m∠AOB = 53°

Step-by-step explanation:

If OA is perpendicular to OC, this means that <AOC = 90°

Given

m∠BOC=6x−6

m ∠AOB = 5 x + 8

The expression is true

m∠BOC+m∠AOB= m∠AOC

6x-6+5x+8 = 90

Find x:

11x + 2 = 90

11x = 90-2

11x = 88

x = 88/11

x =8

Get m∠BOC:

m∠BOC= 6x-6

m∠BOC= 6(8)-11

m∠BOC = 48-11

m∠BOC= 37°

Get m∠AOB;

m∠AOB = 90-m∠BOC

m∠AOB =90-37

m∠AOB = 53°