Exercise 3 Page 311

It is given that m∠ 1=94^(∘). Using this given information, we need to find the measure of angle ∠ 4. Let's begin by recognizing where these angles are on the given diagram.

Angles 1 and 4 are formed by the parallel lines m and n, and the transversal t. They lie on the same side of the transversal but are on different sides of the parallel lines. The two angles in question are called exterior angles, but they are not alternate exterior angles. Because of this, we can calculate m∠ 4 in two steps.

1. We will use the Corresponding Angles Postulate, to find the measure of ∠ 3. In a previous exercise, we found that m∠ 3=94^(∘).
2. Then, we can use the fact that ∠ 3 and ∠ 4 are supplementary angles and the sum of their measures is 180^(∘).

m∠ 3+ m∠ 4=180 Substituting the measure of angle ∠ 3 as 94^(∘) into the above equation, we can calculate the measure of ∠ 4.

m∠ 3+ m∠ 4=180

Substitute

m∠ 3= 94

94+m∠ 4=180

SubEqn

LHS-94=RHS-94

m∠ 4=86

We have found the fhe measure of angle ∠ 4 to be 86^(∘).