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@psi9epsilon or @TheMind you guys wre the most help on teaching me.

EBC = 105 degrees
EBG = 50 degress
You tell me if they are acute, obtuse, or right angles.

Thank you !!! I have one more if you don't mind?(:

Sure. I will see what I can do. Just tag me in the question.

If mangle_AOC= 85°, mangle_BOC = 2x + 10, and mangle_AOB = 4x – 15, find the degree measure of angle_BOCand angle_AOB. The diagram is not to scale.

For this you just add the angles of AOB and BOC together.
4x -15 + 2x + 10 = 85
Try to finish it.

I got x=15?

Yep. Very good. Now take the two separate equations and plug 15 into x.

for BOC= 40 degrees and for AOB=45 degrees is what I got?

Your correct. Nice job.

Thank you !!

No problem. Any time