Question

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

A parallelogram quadrilateral in which opposite sides are parallel is called a parallelogram. The measure of ∠SRV is 48°.

What is a parallelogram?

A parallelogram quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

The diagram for the given condition can be made as shown below. Now in ΔTVU the sum of the measure of the angles can be written as,

∠TVU + ∠VTU + ∠TUV = 180°

∠VTU = 48°

Now, since the given polygon is a parallelogram RS║TU, therefore, the measure of ∠SRV will be equal to ∠VTU because the two angles are a pair of alternate interior angles. Therefore,

∠SRV = ∠VTU = 48°

Hence, the measure of ∠SRV is 48°.

Learn more about Parallelogram:

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