Question

question 4 (essay worth 10 points) (wc) 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.

Explanation:

Step1: Find $\angle STV$ in $\triangle SVT$

Sum of angles in a triangle is $180^\circ$.
$\angle STV = 180^\circ - \angle TSV - \angle SVT = 180^\circ - 31^\circ - 126^\circ = 23^\circ$

Step2: Use parallelogram parallel sides

$RS \parallel UT$, so alternate interior angles are equal.
$\angle URV = \angle STV$

Step3: Assign the calculated value

$\angle URV = 23^\circ$

Answer:

$\boldsymbol{23^\circ}$