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°.
Lines AC and BD intersect at point O.
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°
1 answer