Question

guided practice: angles in parallel lines
b. describe how to use m∠rhb = 51° to find m∠xhr.
c. explain why knowing one of the angles in parallel lines allows you to find all of the angles.

Explanation:

b. If $\angle RHB = 51^{\circ}$, and assuming lines are parallel, $\angle XHR$ and $\angle RHB$ are supplementary (linear - pair of angles on a straight - line). So, $m\angle XHR=180^{\circ}- 51^{\circ}=129^{\circ}$.
c. When lines are parallel, there are angle - relationships like corresponding angles, alternate interior angles, alternate exterior angles, and same - side interior angles. If one angle is known, we can use these relationships (e.g., corresponding angles are equal, alternate interior angles are equal, same - side interior angles are supplementary) to find all other angles.

Answer:

b. $m\angle XHR = 129^{\circ}$
c. When lines are parallel, angle - relationships (corresponding, alternate, supplementary) allow finding all angles from one known angle.