Exercise 48 Page 352

Let's label the angles where the measure is given and focus on angle ∠ 2, along with the angle adjacent to it.

Notice that angles ∠ 2 and ∠ 4 together form a straight angle, so their measures add to 180. Since the measure of ∠ 4 is given on the figure, this allows us to find the measure of ∠ 2.

m∠ 2+m∠ 4=180

Substitute

m∠ 4= 74

m∠ 2+ 74=180

SubEqn

LHS-74=RHS-74

m∠ 2=106

The measure of ∠ 2 is 106^(∘).