Exercise 51 Page 430

We have two complementary angles, which we call ∠ A and ∠ B. We can write the sum and difference of the angle measures. m∠ A + m∠ B m∠ A - m∠ B The sum of the measures of the angles is 74^(∘) greater than the difference between the measures. Therefore, we can write an equation using the expressions for the sum and the difference. m∠ A - m∠ B + 74^(∘) = m∠ A + m∠ B Let's use this to find m∠ B.

m∠ A - m∠ B + 74^(∘) = m∠ A + m∠ B

SubEqn

LHS-m∠ A=RHS-m∠ A

- m∠ B + 74^(∘) = m∠ B

AddEqn

LHS+m∠ B=RHS+m∠ B

74^(∘) = 2* m∠ B

DivEqn

.LHS /2.=.RHS /2.

37^(∘) = m∠ B

RearrangeEqn

Rearrange equation

m∠ B = 37^(∘)

Since ∠ A and ∠ B are complementary, the sum of their measures is 90^(∘).

m∠ A + m∠ B = 90^(∘)

Substitute

m∠ B= 37^(∘)

m∠ A + 37^(∘) = 90^(∘)

SubEqn

LHS-37^(∘)=RHS-37^(∘)

m∠ A = 53^(∘)