Lines AC and BD intersect at point O.

Question

Lines AC and BD intersect at point O.

If m∠AOD = (7x − 5)° and m∠BOC = (3x + 15)°, what is m∠BOC?

5°
30°
39°
60°

Answer 1

To find the measure of angle BOC, we need to use the fact that angles on a straight line add up to 180°.

Since lines AC and BD intersect at point O, we know that angles AOD and BOC are adjacent angles on a straight line. Therefore, the sum of their measures is 180°.

m∠AOD + m∠BOC = 180°

Substituting the given values, we have:

(7x - 5) + (3x + 15) = 180

Combining like terms, we get:

10x + 10 = 180

Subtracting 10 from both sides, we have:

10x = 170

Dividing both sides by 10, we get:

x = 17

Now, we can find the value of m∠BOC by substituting x = 17 into the expression (3x + 15):

m∠BOC = (3x + 15)°
m∠BOC = (3 * 17 + 15)°
m∠BOC = (51 + 15)°
m∠BOC = 66°

Therefore, the measure of angle BOC is 66°.