Two parallel lines are crossed by a transversal.

Question

Horizontal and parallel lines y and z are cut by transversal x. At the intersection of lines y and x, the top right angle is (2 k + 11) degrees. At the intersection of lines z and x, the bottom left angle is 131 degrees.
What is the value of k?

k = 9  
k = 20
k = 60
k = 71

GPT-4o mini · Answer

To solve for $ k $, we need to understand the relationship between the angles formed by the transversal crossing two parallel lines. Given: - The top right angle at the intersection of lines $ y $ and $ x $ is $ (2k + 11) $ degrees. - The bottom left angle at the intersection of lines $ z $ and $ x $ is $ 131 $ degrees. Since lines $ y $ and $ z $ are parallel, the angles formed by the transversal $ x $ have specific relationships. The angle at the top right where line $ y $ intersects line $ x $ and the angle at the bottom left where line $ z $ intersects line $ x $ are corresponding angles, which means they are equal. Thus, we can set up the equation: $$ (2k + 11) = 131 $$ Next, we solve for $ k $: 1. Subtract $ 11 $ from both sides: $$ 2k = 131 - 11 $$ $$ 2k = 120 $$ 2. Divide by $ 2 $: $$ k = \frac{120}{2} = 60 $$ Therefore, the value of $ k $ is: $$ \boxed{60} $$