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.
