Question

In parallelogram RSTU, if the measure of angle TSV is 31° and the measure of angle SVT is 126°, explain how you can find the measure of angle URV. Show the steps of your work and refer to any properties of parallelograms or triangle congruency theorems as necessary to justify your response.

Answer 1

To find the measure of angle URV in parallelogram RSTU, use the property that opposite angles in a parallelogram are equal. Therefore, angle URV = 203°.

Step-by-step explanation:

To find the measure of angle URV in parallelogram RSTU, we can use the property that opposite angles in a parallelogram are equal. Since angle TSV and angle SVT are given, we can conclude that angle TSV = angle SVT. Therefore, angle TSV = 31° and angle SVT = 126°.

Since the opposite angles are equal, we can also conclude that angle RUS = angle TSU = 31° and angle USR = angle UTS = 126°.

Finally, to find the measure of angle URV, we can use the property that the sum of all angles in a quadrilateral is 360°. Since we already know the measures of angle RUS and angle USR, we can subtract their sum from 360° to find the measure of angle URV.

Therefore, angle URV = 360° - (angle RUS + angle USR) = 360° - (31° + 126°) = 360° - 157° = 203°.