Quadrilateral RSTU, diagonals SU and RT intersect at point V. RSTU is a parallelogram. If m∠SRV = 48° and m∠SVR = 54°, explain how you can find the measure of ∠TUV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response. (10 points)

Angle TUV equals 78

Step-by-step explanation:

First you have to use alternate interior angles. the 48 degrees on SRV is also 48 on UTV. We also know about vertical angles. The 54 degrees on angle SVR is also 54 degrees on angle TVU. Now we have two angles done. The Triangle Sum Theorem states that all triangles must add up to 180 degrees. Since we already have to angles we can add those and then subtract that from 180. So you get 180 - 102 = 78. So we get 78 degrees as the third angle.