A carpenter cut the top section of a window frame with a 37 degree angle on each end. The side pieces each have a 50 degree angle cut at their top ends, as shown. Will the side pieces of the frame be parallel? Explain.

The side pieces will not be parallel when lapped with top section ends
because the corresponding angle formed by the side pieces are not equal.
Reasons:
The given angle on each end of the window frame = 37°
The angle at the top ends of the side pieces = 50°
According to angle addition postulate, we have;
Angle formed when the top section and the side pieces lap = 37°+ 50° = 87°
Therefore;
The angle formed by the left side piece is 87° below the positive x-axis
direction, while the corresponding angle formed by the right side piece is
1.3° below the positive x-direction, such that the two side pieces are
inclined towards each other, and given that the corresponding angles are
not equal, the side pieces are therefore, not parallel.
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