Question

Please help!

Geometry
If mZAOC = 31°, mZBOC = 2x + 10, and mZAOB = 4x - 15, find the degree measure of ZBOC and ZAOB.

The diagram is not to scale.

A step by step explanation would be greatly appreciate :(

Answer 1

The measures of ∠BOC is 25.4° and that of ∠AOB is 15.8°.

Explanation:

Given that,

∠AOC = 31°

∠BOC = 2x+10

∠AOB = 4x-15

As we can seen from the figure that,

∠AOC = ∠AOB + ∠BOC

Put all the values,

31 = 4x-15+2x+10

31 = 6x-15

31+15 = 6x

46 = 6x

x = 7.7

∠BOC = 2(7.7)+10 = 25.4°

∠AOB = 4(7.7)-15 = 15.8°

So, the measures of ∠BOC is 25.4° and that of ∠AOB is 15.8°.