Chapter Review: Synthesizing Lines And Angles

In a geometric construction involving parallel horizontal lines and multiple transversals, you are given that $\angle ABC = 45^\circ$ and $\angle IKJ = 78^\circ$. Using the properties of transversals and parallel lines, find the final measures of $\angle GEH$, $\angle HEF$, and $\angle FED$.

Find the measure of angle NOP ($a^\circ$) in a zig-zag path between two parallel rays LM and PQ. You are given $\angle MLN = 40^\circ$, $\angle LNO = 96^\circ$, and $\angle OPQ = 52^\circ$. Hint: Draw imaginary lines parallel to LM and PQ through points N and O.