Exercise 3 Page 363

Let's label the given angles and concentrate on the triangle on the left, with angle ∠ 3 as one of its angles.

Notice that in this triangle the measure of two interior angles is given. We can use the Triangle Angle-Sum Theorem to find the measure of angle ∠ 3, the third interior angle.

m∠ 3+m∠ 4+m∠ 5=180

SubstituteII

m∠ 4= 42, m∠ 5= 72

m∠ 3+ 42+ 72=180

▼

Solve for m∠ 3

AddTerms

Add terms

m∠ 3+114=180

SubEqn

LHS-114=RHS-114

m∠ 3=66

The measure of angle ∠ 3 is 66^(∘).