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°.
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.
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