Exercise 34 Page 53

Let's call the unknown 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 measure of one angle is 3^(∘) more than 12 the measure of its supplement. Assume that ∠ A is the larger angle, and let's call its measure x. We then we have the following expressions for the measures of the unknown angles. m∠ A =& x [0.5em] m∠ B =& 12x+ 3 Substituting these values into the sum gives us the desired algebraic equation. m∠ A + m∠ B &= 180 x+ (1/2x+3) &= 180 Now we can solve for x and find the measures of the angles.

m∠ A + m∠ B = 180^(∘)

SubstituteII

m∠ A= x, m∠ B= 1/2x+3

x + 1/2x+3 = 180

AddTerms

Add terms

1 12x+3=180

SubEqn

LHS-3=RHS-3

1 12x=177

▼

Write mixed number as a fraction

MixedToFrac

a bc=a* c+b/c

2+1/2x=177

AddTerms

Add terms

3/2x=177

MultEqn

LHS * 2=RHS* 2

3x=354

DivEqn

.LHS /3.=.RHS /3.

x=118

Knowing that x=118^(∘), we can determine the measures of the angles. &m∠ A ⇒ x= 118^(∘) &m∠ B ⇒ 1/2x+3= 1/2( 118)+3=62^(∘)