Exercise 7 Page 427

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 bigger angle is twice as large as 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 =& 2x Now we can substitute these values into our equation and solve for x.

m∠ A + m∠ B = 90

SubstituteII

m∠ A= x, m∠ B= 2x

x + 2x = 90

AddTerms

Add terms

3x=90

DivEqn

.LHS /3.=.RHS /3.

x=30

Knowing that x=30^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 30^(∘) &m∠ B ⇒ 2x= 2( 30)=60^(∘)