Exercise 22 Page 429

Let's call the unknown angles ∠ A and ∠ B. We know that ∠ A and ∠ B are complementary and, therefore, the sum of their measures is 90^(∘). m∠ A + m∠ B = 90^(∘) We are told that the measure of one angle is 14 the measure of its compliment. Assume that ∠ A is the smaller angle and let's call its measure x. Rather than thinking of the smaller angle as 14 of the measure of the larger angle, we can think of the larger angle as 4 times the measure of the smaller one. m∠ A =& x m∠ B =& 4x Now we can substitute these values into our equation and solve for x.

m∠ A + m∠ B = 90^(∘)

SubstituteII

m∠ A= x, m∠ B= 4x

x + 4x = 90

AddTerms

Add terms

5x=90

DivEqn

.LHS /5.=.RHS /5.

x=18

Knowing that x=18^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 18^(∘) &m∠ B ⇒ 4x= 4( 18)=72^(∘)