Exercise 21 Page 434

Two angles are supplementary if the sum of their measures is 180^(∘). With this in mind, we can create an equation to demonstrate this relationship. m∠ 3 + m∠ 4= 180^(∘) We can find m∠ 4 by substituting the given value, m∠3=116^(∘), into the equation.

m∠ 3 + m∠ 4= 180^(∘)

Substitute

m∠ 3= 116^(∘)

116^(∘) + m∠ 4= 180^(∘)

SubEqn

LHS-116^(∘)=RHS-116^(∘)

m∠ 4= 64^(∘)

The measure of ∠ 4 is 64^(∘).