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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:
- 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]
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