One of the angles formed by two intersecting lines is 42°. what is the measure of the other three angles?

Okay, so first lets think about the angle next to the 42 degree angle.
we know that those two angles must add to 180 degrees, so lets form an equation to figure out the other angle
42 + x = 180
subtract 42 from both sides
x = 138
so 138 degrees is the first AND the 3rd angle
the opposite angle from the 42 degree angle also happens to be 42 degrees

this is because there are two lines in total right?? if you draw out the 42 degree angle and the 138 degree angle, flip that upside down, the angles are the same!!

i hope this helps!! 

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