Exercise 50 Page 352

Let's label the angles where the measure is given and focus on the lower triangle. This is a right triangle, where the measure of one of the acute angles is given and we are asked to find the measure of the other acute angle.

According to Corollary 4.1 of the Triangle Angle-Sum Theorem, the acute angles of a right triangle are complementary so their measures add to 90^(∘).

m∠ 3+m∠ 4=90

Substitute

m∠ 4= 74

m∠ 3+ 74=90

SubEqn

LHS-74=RHS-74

m∠ 3=16

The measure of ∠ 3 is 16^(∘).