In the diagram below line m is parallel to line n what is the measure of 142 52 38 90

You need to find the angle measurements of the triangle.
The angle supplementary to 128 measures (180 - 128 =) 52 degrees.

Using the corresponding and supplementary property because lines m and n are parallel, you know that the highest (in location) angle of the triangle measure 90 degrees.

A triangle's total angle measurements add up to 180 degrees. Subtract the other two known angles from 180. 180 - 52 - 90 = 38. The third (right side) angle of the triangle measures 38 degrees. 

Now, using the supplementary angle theorem, you can find angle a, which is supplementary to the third angle on the triangle. 180 - 38 = 142.

Angle a measures 142 degrees.