Examining the given diagram, we can see markings on some angles.They indicate that these angles are congruent. Therefore, ∠T≅∠S. This means that the measure of ∠T is the same as the measure of ∠S, which is 74^(∘).
Now, to find the measure of ∠V, we can use the Triangle Angle-Sum Theorem, which states that measures of the interior angles of a triangle add to 180^(∘). Since ∠U is a right angle, △ TUV is a right triangle. Therefore, the acute angles are complementary. In this case, this means that m∠T and m∠V add to 90^(∘).
m∠T + m∠V = 90^(∘)
By solving this equation, we can find the measure of ∠V.
