Hello!
We know that angle AOC = 79 degrees, AOB = 4x - 15, and BOC = 2x+10. If you observe the picture, you can notice that the two other angles make up AOC.
Therefore, the measure of AOC = the measure of AOB + the measure of BOC. Now, we can create our equation with this info.
79 = (4x - 15) + (2x + 10)
Now, simplify.
79 = 4x - 15 + 2x + 10
79 = 6x - 5
84 = 6x
x = 14
Now, to find the individual degree measurements, substitute in 14 for x and solve.
AOB: 4x - 15 = 4(14) - 15 = 56 - 15 = 41 degrees
BOC: 2x + 10 = 2(14) + 10 = 28 + 10 = 38 degrees
Therefore, your answer is B, BOC = 38 degrees and AOB = 41 degrees.
Hope this helps!
