In the figure shown, line ab is parallel to line cd.
explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal.

Part A:

The measurement for angle x is might be 46. I think this is correct because Parallel lines AB and CD are cut by a transversal PR.  

Part B:

Look at the angle <PRD = 110. It will be supplementary to the consecutive interior angle <RPB, so it must be 70 Now you have 3 angles that form a straight line at the top. 64 + x + 70 = 180° x = 180 - 134 x = 46° x = 46

Step-by-step explanation:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal