Line AC intersects Line BD at point O.

Question

Line A C intersects Line B D at point O.

If m∠AOB = (6x − 14)° and m∠BOC = (2x + 2)°, what is m∠BOC?

10°
24°
50°
130°

Answer 1

m∠BOC = (2x + 2)°

Given that m∠AOB = (6x − 14)°, the sum of m∠BOC and m∠AOB must add up to 180° since they form a straight line.

Therefore, (6x - 14) + (2x + 2) = 180
8x - 12 = 180
8x = 192
x = 24

Substitute x = 24 into the equation for m∠BOC:
m∠BOC = (2(24) + 2)°
m∠BOC = 50°

So, m∠BOC = 50°.