Question

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

RSTU is a parallelogram. If m∠TUV = 78° and m∠TVU = 54°, explain how you can find the measure of ∠SRV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of ∠SRV, we can use the properties of parallelograms and the Triangle Angle Sum Theorem.

Since RSTU is a parallelogram, opposite angles are congruent. This means ∠R = ∠U and ∠S = ∠T.

Since SU and RT are diagonals of parallelogram RSTU and they intersect at point V, we know that triangles SVU and TVR are congruent by the Side-Angle-Side (SAS) congruence theorem.

This means that ∠SVU = ∠TVR, ∠SUV = ∠TVR, and ∠USV = ∠VTR.

Therefore, since we know that ∠TUV = 78° and ∠TVU = 54°, we can find ∠UVT by using the Triangle Angle Sum Theorem:
∠UVT = 180° - 78° - 54°
∠UVT = 48°

Since ∠UVT = ∠SUV = ∠TVR, we now know that ∠SUV = 48°.

Now, we can find ∠SRV by using the Triangle Angle Sum Theorem in triangle SVR:
∠SRV = 180° - ∠SVR - ∠RVS
∠SRV = 180° - 48° - 54°
∠SRV = 78°

Therefore, the measure of ∠SRV is 78°.