Exercise 51 Page 476

Two angles are complementary if the sum of their measures is 90^(∘). Since we are told that ∠1 is a complement of ∠4, we can create an equation to demonstrate this relationship. m∠ 1 + m∠ 4= 90^(∘) We can find m∠ 4 by substituting the given value, m∠ 1=33^(∘), into the equation.

m∠ 1 + m∠ 4= 90^(∘)

Substitute

m∠ 1= 33^(∘)

33^(∘) + m∠ 4= 90^(∘)

SubEqn

LHS-33^(∘)=RHS-33^(∘)

m∠ 4= 57^(∘)

The measure of m∠ 4 is 57^(∘).