Question

RSTU is a parallelogram. If m∠SRV = 48° and m∠SVR = 54°, how can you find the measure of ∠TUV?

a) Measure m∠TUV as 54°.
b) Measure m∠TUV as 96°.
c) Measure m∠TUV as 126°.
d) Measure m∠TUV as 48°.

Answer 1

By utilizing the properties of triangles and parallelograms, ∠TUV in parallelogram RSTU is determined to have a measure of 126°, making option (c) the correct answer.

Step-by-step explanation:

To determine the measure of ∠TUV in parallelogram RSTU, we must understand the properties of parallelograms and triangles. Given that ∠SRV = 48° and ∠SVR = 54°, these are angles in triangle SRV. Since the sum of angles in any triangle is 180°, the measure of ∠VSR can be found using the equation 180° - (48° + 54°) = 180° - 102° = 78°.

Now considering parallelogram RSTU, we know that opposite angles are equal (∠R=∠U and ∠S=∠T), and consecutive angles are supplementary (∠R + ∠S = 180°). Because ∠R = ∠SVR = 54°, ∠S must be 180° - 54° = 126°. Since ∠S and ∠TUV are alternate interior angles formed by the diagonal SU cutting across parallel lines ST and UV, they are equal. Therefore, ∠TUV = ∠S = 126°. The correct answer to the student's question would be (c) Measure ∠TUV as 126°.