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

Find the value of x in each case. Give reasons to justify your solutions!-example-1

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Answer:

x = 11°

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

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