Exercise 8 Page 427

Let's call the unknown linear pair of Angles ∠ A and ∠ B. We know that ∠ A and ∠ B are supplementary and, therefore, the sum of their measures is 180^(∘). m∠ A + m∠ B = 180 We are told that the bigger angle is one and a half times 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 =& 1.5x Now we can substitute these values into our equation and solve for x.

m∠ A + m∠ B = 180

SubstituteII

m∠ A= x, m∠ B= 1.5x

x + 1.5x = 180

AddTerms

Add terms

2.5x=180

DivEqn

.LHS /2.5.=.RHS /2.5.

x=72

Knowing that x=72^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 72^(∘) &m∠ B ⇒ 1.5x= 1.5( 72)=108^(∘)