Question

lines hx and sp intersect line rt as shown. which of the following statements are true? select all that apply. □ ∠bvr and ∠swv are corresponding angles □ ∠bvw and ∠wvx are alternate interior angles □ ∠rvx and ∠swt are alternate interior angles □ ∠swv and ∠twp are alternate exterior angles □ ∠rvx and ∠wvx are consecutive angles □ ∠wvx and ∠vwp are alternate exterior angles

Explanation:

Step1: Recall angle - pair definitions

Alternate interior angles are non - adjacent angles between two lines and on opposite sides of a transversal. Alternate exterior angles are non - adjacent angles outside two lines and on opposite sides of a transversal. Corresponding angles are in the same relative position with respect to the lines and the transversal. Consecutive angles are on the same side of the transversal.

Step2: Analyze each option

• For $\angle RVX$ and $\angle SWT$: They are alternate interior angles as they are between the lines $SP$ and $HX$ and on opposite sides of the transversal $RT$.
• For $\angle SWV$ and $\angle TWP$: They are alternate exterior angles as they are outside the lines $SP$ and $HX$ and on opposite sides of the transversal $RT$.
• For $\angle WVX$ and $\angle VWP$: They are consecutive interior angles (not alternate exterior angles).
• For $\angle RVX$ and $\angle WVX$: They are adjacent angles, not consecutive angles in the sense of parallel - line transversal relationships.
• For $\angle BVW$ and $\angle WVX$: They are adjacent angles, not alternate interior angles.
• For $\angle BVR$ and $\angle SWV$: They are corresponding angles as they are in the same relative position with respect to the lines $SP$ and $HX$ and the transversal $RT$.

Answer:

• $\angle RVX$ and $\angle SWT$ are alternate interior angles.
• $\angle SWV$ and $\angle TWP$ are alternate exterior angles.
• $\angle BVR$ and $\angle SWV$ are corresponding angles.