Exercise 29 Page 326

It is given that m∠ 1=123. Using this information, we need to find the measure of ∠ 4. Let's find these angles on the given diagram.

These angles are formed by two parallel lines and the transversal. They lie on the same side of the transversal but on different sides of the parallel lines. These 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. We conclude that ∠ 1 and ∠ 3 are congruent, so their measures are the same. Therefore, the measure of ∠ 3 is also 123.
2. Then, we can use 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 123 into the above equation, we can calculate the measure of ∠ 4.

m∠ 3+ m∠ 4=180

Substitute

m∠ 3= 123

123 +m∠ 4=180

SubEqn

LHS-123=RHS-123

m∠ 4=57

The measure of ∠ 4 is 57.