Question

6 multiple choice 5 points in the diagram below, lines p and r are parallel. line s is a transversal that is not perpendicular to lines p and r. which angle is not congruent to ∠5? ∠7 ∠1 ∠3 ∠2

Explanation:

Step1: Vertical angles

Vertical angles are congruent. So, $\angle5\cong\angle7$.

Step2: Corresponding angles

Since $p\parallel r$, corresponding angles are congruent. $\angle1$ and $\angle5$ are corresponding angles, so $\angle1\cong\angle5$.

Step3: Alternate - interior angles

Since $p\parallel r$, alternate - interior angles are congruent. $\angle3$ and $\angle5$ are alternate - interior angles (because $p\parallel r$ and $s$ is the transversal), so $\angle3\cong\angle5$.

Step4: Adjacent angles

$\angle2$ and $\angle5$: $\angle2$ and $\angle1$ are adjacent and form a linear pair ($\angle1+\angle2 = 180^{\circ}$). Since $\angle1\cong\angle5$, if $\angle2\cong\angle5$, then $\angle1+\angle5=180^{\circ}$ (which would mean $s\perp p$, but we know $s$ is not perpendicular to $p$ and $r$).

Answer:

$\angle2$