Exercise 7 Page 111

Looking at the figure, we notice three things we need to figure out the remaining angles.

1. ∠ 1 and ∠ 3 are vertical angles.
2. ∠ 1 is supplementary to both ∠ 2 and ∠ 4.
3. ∠ 2 and ∠ 4 are vertical angles.

By the Vertical Angles Congruence Theorem, ∠ 3 and ∠ 1 are congruent. m∠ 3 =m∠ 1 As m∠ 1 =143^(∘), it must follow that m∠ 3 =143^(∘). Supplementary angles have measures that sum to 180^(∘). Additionally, since we also know that ∠ 2 and ∠ 4 are vertical angles, we can write the following three equations. m∠ 1+m∠ 2&=180 m∠ 1+m∠ 4&=180 m∠ 2&=m∠ 4 By solving the first equation for m∠ 2, we also figure out the measure of ∠ 4.

m∠ 1+m∠ 2=180

Substitute

m∠ 1= 143

143+m∠ 2=180

SubEqn

LHS-143=RHS-143

m∠ 2=37

Let's summarize what we have found. m∠ 2&=37^(∘) m∠ 3&=143^(∘) m∠ 4&=37^(∘)