Exercise 1 Page 363

Let's label the given angles and concentrate on the part of the figure that is connected to angle ∠ 1, the measure of which we are asked to find.

Notice that angles ∠ 5 and ∠ 1 form a linear pair, so their measures add to 180^(∘). Since the measure of angle ∠ 5 is given on the figure, this lets us find the measure of angle ∠ 1.

m∠ 5+m∠ 1=180

Substitute

m∠ 5= 72

72+m∠ 1=180

SubEqn

LHS-72=RHS-72

m∠ 1=108

The measure of angle ∠ 1 is 108^(∘).