1 and 2 are complementary angles. 1 and 3 are vertical angles. If m2=52, what is the measure of the SUPPLEMENT to angle 3?

If angle 1 and angle 2 are complementary, then they add up to 90 degrees. We are given that angle 2 equals 52 degrees.

So we subtract and get our

38

That's NOT the final answer.

The next step is:

Angle 1 and angle 3 are vertical angles.

Vertical angles are congruent.

So if angle 1 is 38, then angle 3 is also 38.

Now, supplementary angles add up to 180 degrees.

So that's the

180-38=142

142 is the supplement of angle 3.

Hope it helps! :)

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