Question

transversal t cuts parallel lines r and s. which angles must be congruent to \\( \angle 2 \\)?
a. \\( \angle 3, \angle 6, \\) and \\( \angle 7 \\)
b. \\( \angle 7 \\) only
c. \\( \angle 7 \\) and \\( \angle 6 \\)
d. \\( \angle 3, \angle 5 \\) and \\( \angle 6 \\)

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. $\angle2$ and $\angle4$ are vertical angles, so $\angle2\cong\angle4$.

Step2: Use parallel - line properties (alternate interior angles)

Since $r\parallel s$ and $t$ is a transversal, alternate interior angles are congruent. $\angle4\cong\angle6$ (alternate interior angles).

Step3: Use parallel - line properties (corresponding angles)

Also, $\angle2$ and $\angle7$ are corresponding angles. When $r\parallel s$ and $t$ is a transversal, corresponding angles are congruent, so $\angle2\cong\angle7$.

Answer:

B. $\angle7$ only