RSTU is a parallelogram. If m∠TSV = 31° and m∠SVT = 126°, explain how you can find the measure of ∠URV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

∠URV = 23°

Step-by-step explanation:

Given that:

RSTU is a parallelogram. If m∠TSV = 31° and m∠SVT = 126°

The objective is to explain how you can find the measure of ∠URV.

The diagrammatic expression of the parallelogram can be seen in the attached file below.

From the diagram , if we take a look at ΔSVT;

∠TSV + ∠SVT + ∠VTS = 180°    ( sum of angles in a triangle = 180° )

31° + 126° + ∠VTS = 180°

157° + ∠VTS = 180°

∠VTS = 180° - 157°

∠VTS = 23°

For a parallelogram, the opposite sides are parallel to each other. From the diagram  below , we can say that  ST || RU   ( parallel lines are equal)

Also, the alternate angles between two parallel lines formed by a transverse line are equal.  

From the RSTU parallelogram seen below, ∠VTS and ∠URV are alternate angles between the parallel lines ST and RU which is formed by the transversal RT.

Hence;

∠URV = ∠VTS     ( alternate angles)

∠URV = 23°