Quadrilateral RSTU, diagonals SU and RT intersect at point V. 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:

If we look at the diagram we find that there is a triangle  SVT formed by the diagonals and the base of the parallelogram.

As all the angles of the triangle SVT must be equal to 180 degrees therefore we can find the third angle by adding the other two known angles and subtracting them from 180 degrees.

Hence

m ∠VTS + m∠TSV+ m∠SVT= 180°

m ∠VTS = 180°-31°- 126°

m ∠VTS = 23°

If we extend the diagonal RT and also increase the other lines we find that it acts as a transversal of the lines RU and ST.

As the alternate interior angles of the transversal are equal  the angles

m∠URV=  m ∠VTS  are also equal .

Therefore m∠URV=  23°

as

m ∠VTS=  23°

m∠URV=  m ∠VTS  are alternate angles.

answer is 67%

step-by-step explanation:

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

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