Question

note: figure not drawn to scale. in the figure shown, lines r and s are parallel, and line m intersects both lines. if y < 65, which of the following must be true? a) x < 115 b) x > 115 c) x + y < 180 d) x + y > 180

Explanation:

Step1: Use property of parallel lines

Since lines $r$ and $s$ are parallel and line $m$ is a transversal, $x + y=180^{\circ}$ (co - interior angles).

Step2: Analyze the given condition

Given $y < 65$. Then $x=180 - y$. Substituting the inequality for $y$, we get $x>180 - 65$. So $x > 115$.

Answer:

B. $x > 115$