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Please help me find the measure of m

Please help me find the measure of m-example-1

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See angle AOC.

It starts at the horizontal 180 degrees and goes to 150 degrees.

It is an acute angle.

Thus, it's measure is:

180 - 150 = 30 degrees

Thus,


m\angle\text{AOC}=30\degree

Now, see angle COE.

It starts at 150 degrees and entends to 40 degrees. It is an obtuse angle (greater than 90). Thus, the angle is:

150 - 40 = 110 degrees

Thus,


m\angle\text{COE}=110\degree

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