Find the value of x in each case. Give reasons to justify your solutions!

Answer:
x = 11°
Step-by-step explanation:
The parallel lines suggest we look to the relationships involving angles and transversals. The angle marked 33° and ∠CAB are alternate interior angles, hence congruent:
∠CAB = 33°
5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:
5x = 2x + 33°
3x = 33° . . . . . . . . . subtract 2x
x = 11° . . . . . . . . . . . divide by 3