Exercise 8 Page 428

Two angles are complementary if the sum of their measures is 90^(∘). Since we are told that ∠3 is a complement of ∠4, we can create an equation to demonstrate this relationship. m∠ 3 + m∠ 4= 90^(∘) We can find m∠ 4 by substituting the given value, m∠3=46^(∘), into the equation.

m∠ 3 + m∠ 4= 90^(∘)

Substitute

m∠ 3= 46^(∘)

46^(∘) + m∠ 4= 90^(∘)

SubEqn

LHS-46^(∘)=RHS-46^(∘)

m∠ 4= 44^(∘)

The measure of ∠ 4 is 44^(∘).