Exercise 19 Page 428

Let's call the unknown angles ∠ A and ∠ B. We know that ∠ A and ∠ B form a linear pair and, therefore, they are supplementary angles. Since the sum of measures of supplementary angles is 180^(∘), we can write an equation. m∠ A + m∠ B = 180^(∘) We are told that one 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 = 180^(∘)

SubstituteII

m∠ A= x, m∠ B= 2x

x + 2x = 180

AddTerms

Add terms

3x=180

DivEqn

.LHS /3.=.RHS /3.

x=60

Knowing that x=60^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 60^(∘) &m∠ B ⇒ 2x= 2( 60)=120^(∘)