When lines a and b are cut by transversal d , and are a pair of alternate exterior angles that are formed. If and , find x .
A)x = 3
B)x = 3.5
C)x = 4
D)x = 4.5

Question

When lines a and b are cut by transversal d ,  and  are a pair of alternate exterior angles that are formed. If  and  , find x .
A)x = 3 
B)x = 3.5 
C)x = 4 
D)x = 4.5

Quizplus · Accepted Answer

By the alternate exterior angles theorem, 11ebfb55_2499_99ed_9d86_2bd15d508962_TBX8811_11 and 11ebfb55_2499_99ee_9d86_716fd50330e2_TBX8811_11 are congruent, meaning that m∠1 = m∠2. Also, because angles 1 and 2 are corresponding angles, we have m∠1 = x + 2 and m∠2 = 5x - 12. Therefore, x + 2 = 5x - 12, and solving for x gives x = 4.

When Lines a and B Are Cut by Transversal D