Point O is the incenter of ΔABC. What is mQBO? mQBO is ___ degrees.

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Question:

Point O is the incenter of ΔABC. What is mQBO? mQBO is ___ degrees.

Answer:

Ok, so you already know that mQBO = 3x-15°
You just need to find x. 

You use mSAO and mQAO to solve for x. You can also see that triangle AOS and triangle AQO are similar. Solve these two equations for x and mAOQ:

90+(2x+6)+mAOQ = 180
90+(4x-12)+mAOS = 180

x=9 and mAOQ=mAOS=66°

Now you can find mQBO, by simple algebra: 
3x-15=3*9-15=12

So, mQBO is12 degrees.

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