Asked by Marisol

B is in the interior of <AOC. C is in the interior of <BOD. D is in the interior of <COE. m<AOE=162, m<COE=68, and m<AOB=m<COD=m<DOE. Find m<DOA.

I have a sketch of the angles, and this is what I have so far as for work:

162=68+3x
94=3x
x=31.3
x is the measure of the three equal angles, but not DOA. I'm not sure what to do after this. Help?

Thanks!
Answered by Reiny
According to your description in my diagram AD bisects angle COE, so 2x = 68
and x = 34

then 3x + angle BOC = 162
angle BOC = 162-3(34) = 102

Then angle DOA = 34+102+34 = 170
Answered by Marisol
Wait, I'm confused. How does the angle equal more than what the entire thing is, which is m<AOE=162? Or did I sketch this wrong?
Answered by Reiny
You are right for catching that!

My error is in the second last line

angle BOC = 162-3(34) = 60 , (not 102)
and

Then angle DOA = 34+60+34 = 128

Answered by Marisol
word
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