Exercise 56 Page 314

Let's look at the given diagram.

From the given statement we know that angles ∠ 6 and ∠ 8 are complementary. Therefore their measures add to 90. m∠ 6 + m∠ 8 = 90 We are also told that m∠ 8=47. We can find m∠ 6 by substituting m∠ 8 = 47 into this equation.

m∠ 6 + m∠ 8 = 90

Substitute

m∠ 8= 47

m∠ 6 + 47 = 90

SubEqn

LHS-47=RHS-47

m∠ 6 = 43

Moreover, we can see that ∠ 6, ∠ 7, and ∠ 8 are supplementary angles. Therefore, the Supplement Theorem gives us the following relation. m∠ 6 + m∠ 7 + m∠ 8 = 180 We can find m∠ 7 by substituting m∠ 6=43 and m∠ 8 = 47 into this equation.

m∠ 6 + m∠ 7 + m∠ 8 = 180

SubstituteII

m∠ 6= 43, m∠ 8= 47

43 + m∠ 7 + 47 = 180

AddTerms

Add terms

m∠ 7 + 90 = 180

SubEqn

LHS-90=RHS-90

m∠ 7 = 90

We found that the measure of ∠ 6 is 43 and the measure of ∠ 7 is 90.