Question

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.

Answer 1

Using the triangle sum theorem and the alternate interior angles theorem, the measure of ∠TUV is: 78°

What is the Triangle Sum Theorem?

In any triangle, all three angles have a sum of 180 degrees, based on the triangle sum theorem.

What is the Alternate Interior Angles Theorem?

The alternate interior angles theorem states that if two interior angles lie alternate to each other, both angles have the same measure.

Given the following:

• m∠SRV = 48°
• m∠SVR = 54°

Find m∠RSV using the triangle sum theorem:

m∠RSV = 180 - (m∠SRV + m∠SVR)

m∠RSV = 180 - (48 + 54)

m∠RSV = 78°

∠RSV and ∠TUV are alternate interior angles, therefore:

m∠RSV = m∠TUV = 78° [alternate interior angles theorem]

Learn more about the triangle sum theorem on:

brainly.com/question/7696843

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