Exercise 21 Page 52

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 the bigger angle is 9 times the measure of the smaller angle. Assume that ∠ A is the smaller angle and let's call its measure x. Then we have the following expressions for the measures of the unknown angles. m∠ A =& x m∠ B =& 9x Now we can substitute these values into our equation and solve for x.

m∠ A + m∠ B = 90^(∘)

SubstituteII

m∠ A= x, m∠ B= 9x

x + 9x = 90

AddTerms

Add terms

10x=90

DivEqn

.LHS /10.=.RHS /10.

x=9

Knowing that x=9^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 9^(∘) &m∠ B ⇒ 9x= 9( 9)=81^(∘)