When two parallel lines are cut by a transversal, and are a pair of alternate interior angles formed. If and , find x.
A) x = 5
B) x = 6
C) x = 7
D) x = 8

Question

When two parallel lines are cut by a transversal,  and  are a pair of alternate interior angles formed. If  and  , find x.
A) x = 5 
B) x = 6 
C) x = 7 
D) x = 8

Quizplus · Accepted Answer

By the property of alternate interior angles, we know that 11eb4b36_76da_09e6_a05a_6d5ba1fcd741_TB7237_11 and 11eb4b36_76da_09e7_a05a_8944acb1eb30_TB7237_11 are also alternate interior angles. This means they are congruent to 11eb4b36_76da_09e4_a05a_7164e5b8339e_TB7237_11. Therefore, 2x + 7 = 3x - 4. Solving for x, we get x = 11. However, we need to check if this value makes the two pairs of alternate interior angles equal. Plugging in x = 11, we get 11eb4b36_76da_09e4_a05a_7164e5b8339e_TB7237_11 = 63 and 11eb4b36_76da_09e6_a05a_6d5ba1fcd741_TB7237_11 = 63. Therefore, x = 11 satisfies both conditions and the answer is choice C.

When Two Parallel Lines Are Cut by a Transversal