Question

Please help me find the measure of m

Answer 1

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,

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