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.

Angle SRV equals 48°

Explanation:

1. First, you have to use alternate interior angles. The 78° on TUV is also 78° on angle RSV.

2. Now we do the other angle, which is the vertical angle. The 54° on angle TVU is also 54° on angle SVR. Now these two angles are done.

3. Now, we add our combined two angles to 180°, according to the Triangle Sum Theorem. So, we add up our two angles together and subtract that from 180.  

4. 78 + 54 = 132, so now we subtract that from 180. 180 - 132 = 48. So the third angle is 48°.

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