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.

m∠URV = 23°

Step-by-step explanation:

RSTU is a parallelogram   Given

SU and RT are diagonals

Therefore, SU bisect angle ∠TSR and RT bisects ∠SRU

m∠TSV = 31°  Given

m∠SVT = 126° Given

∴ m∠STV = 180° - (m∠TSV + m∠SVT) = 180° - (126° + 31°) = 23° (Sum of angles in a triangle ΔSVT = 180°)

m∠STV = 23° = m∠URV (Alternate angles of parallel lines RU and ST of parallelogram RSTU)

m∠URV = 23°

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step-by-step explanation: