Lines AC and BD intersect at point O. If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?

Question

Lines AC and BD intersect at point O.

If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?

1. 6° 
2. 53° 
3. 89° 
4. 106°

Answer 1

Angles AOD and BOC are vertical angles and hence are congruent.

Answer 2

The angles AOD and BOC are equal, since they are both supplementary to angle DOC (or, AOB).

So, 10x-7 = 7x + 11, which means x = 6 degrees.

Finally, BOC = 7x + 11 = 53 degrees