Exercise 33 Page 53

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 12^(∘) more than twice the measure of its complement. 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 =& 2x+ 12 Substituting these values into the sum gives us the desired algebraic equation. m∠ A + m∠ B &= 90 x + (2x+12) &= 90 Now we can solve for x and find the measures of the angles.

x+(2x+12)=90

RemovePar

Remove parentheses

x+2x+12=90

AddTerms

Add terms

3x+12=90

SubEqn

LHS-12=RHS-12

3x=78

DivEqn

.LHS /3.=.RHS /3.

x=26

Knowing that x=26^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 26^(∘) &m∠ B ⇒ 2x+12= 2( 26)+12=64^(∘)