Question

Given lines are parallel, find the value of x. Then determine the measure of the angle.

Answer 1

Answers:

• x = 45
• angle measure = 104 degrees

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Explanation:

These angles are on alternating sides of the transversal line, and they are exterior of the parallel lines. Therefore, these are alternate exterior angles.

Alternate exterior angles are congruent when we have parallel lines like this.

Set the two expressions equal to each other. Solve for x.

3x-31 = x+59

3x-x = 59+31

2x = 90

x = 90/2

x = 45

Then we can find that:

• 3x-31 = 3*45-31 = 135-31 = 104
• x+59 = 45+59 = 104

Both alternate exterior angles are 104 degrees each, which confirms we have the correct x value.