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 wo

Question

2 years ago

7

rk, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

1 answer:

Sever21 [200] · Answer 1 · 2023-02-18T17:22:19+03:00

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

<h3>What is the Triangle Sum Theorem?</h3>

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

<h3>What is the Alternate Interior Angles Theorem?</h3>

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:

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:

#SPJ1