It is given that R-M-O, m∠PMO = 78,m∠OMQ = 101, and that rays  and  lie on opposite sides...

It is given that R-M-O, m∠PMO = 78,m∠OMQ = 101, and that rays  and  lie on opposite sides of line

(a) Find the measure of ∠PMQ, establishing all the necessary betweenness relations without using the figure. (You might find the result of Problem 16 useful.)

(b) Find m∠PMQ if m∠PMO = 80, and everything else is the same. Again, establish all betweenness relations used.

(C) If m∠PMO = 79 and everything else is the same, prove that the pair of angles ∠PMO and ∠OMQ are linear.