Question

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 ∘ m∠AOB=5x+8 ∘ m, angle, A, O, B, equals, 5, x, plus, 8, degrees Find m ∠ B O C m∠BOCm, angle, B, O, C:

Answer 1

Answer:

m∠BOC = 40°

Step-by-step explanation:

Given O A ‾ ⊥ O C ‾ OA ⊥ OC m∠BOC=6x−6 ∘

m∠AOB=5x+8 ∘

Find m ∠ B O C:

This means that: m∠BOC and m∠AOC intersect at a right angle.

Hence:

m∠BOC + m∠AOC = 90°

Step 1

Solving for x

6x - 6 + 5x + 8 = 90°

11x -2 = 90°

11x = 90 - 2

11x = 88

x = 88/11

x = 8

Step 2

Solving for m∠BOC

m∠BOC = 6x - 8

m∠BOC = 6(8) - 8

= 48 - 8

= 40°