Exercise 8 Page 111

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

1. ∠ 3 and ∠ 1 are vertical angles.
2. ∠ 3 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∠ 3 =159^(∘) it must follow that m∠ 1 =159^(∘). 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∠ 3+m∠ 4&=180 m∠ 3+m∠ 2&=180 m∠ 2&=m∠ 4 By solving the first equation for m∠ 4, we also figure out the measure of ∠ 2.

m∠ 3+m∠ 4=180

Substitute

m∠ 3= 159

159+m∠ 4=180

SubEqn

LHS-159=RHS-159

m∠ 4=21

Let's summarize what we have found. m∠ 1&=159^(∘) m∠ 2&=21^(∘) m∠ 4&=21^(∘)