Question

given the image, which of these gives enough information to use one of the theorem converses to prove that p || r? m∠5 = 59°. m∠1 = 121°. two of these. m∠2 = 59°. m∠8 = 59°

Explanation:

Step1: Recall parallel - line theorem

If corresponding angles are equal, then the lines are parallel. $\angle5$ and $\angle8$ are corresponding angles.

Step2: Analyze given and options

Given $m\angle5 = 59^{\circ}$. If $m\angle8=59^{\circ}$, by the converse of the corresponding - angles postulate, we can prove that $p\parallel r$.

Step3: Check other options

• Option A: $m\angle1 = 121^{\circ}$ has no direct relation to prove $p\parallel r$ using common parallel - line theorems with the given $m\angle5 = 59^{\circ}$.
• Option B: Just saying "Two of these" is not specific enough.
• Option C: $\angle2$ and $\angle5$ are not corresponding, alternate - interior, or alternate - exterior angles that would directly prove $p\parallel r$ with the given information.

Answer:

D. $m\angle8 = 59^{\circ}$