If m∠AOC=85, m∠BOC=8x+10, and m∠AOB= 4x-15, find m∠BOC and m∠AOB

Question

I am having a hard time understanding how to do this problem. 

 

Thank You. 

Answer 1

Draw a picture with point O in the middle and 3 points in a circle around it. Label the points A, B, and C.

 

Connect A and O

Connect B and O

Connect C and O

 

Mark the angles <AOC=85, <BOC=8x +10, and <AOB=4x -15 

 

From your picture you should see that    m<AOC + m<BOC + m<AOB = 360

 

so                                                             85   + (8x + 10) + (4x -15) = 360

 

Solve for x and plug into (8x +10) and (4x-15)  (check your answers!)