Exercise 33 Page 127

To determine y, we should first recognize that the labeled angles below form a linear pair. This means that the sum of their measures is 180.

Let's solve it for y.

(y+x)+(y-x)=180

▼

Solve for y

RemovePar

Remove parentheses

y+x+y-x=180

AddSubTerms

Add and subtract terms

2y=180

DivEqn

.LHS /2.=.RHS /2.

y=90

Now that we know the value of the y-variable, we can substitute it into the measures of both angles. (y+x)^(∘) ⇒ (90+x)^(∘) (y-x)^(∘) ⇒ (90-x)^(∘) We can consider the diagram once more, including the simplified expressions. Let's label two angles that are vertical.

To determine x, we can use the fact that vertical angles are congruent by the Vertical Angles Theorem. We can equate the expressions for the two angle measures and solve for x.

2x=90-x

▼

Solve for x

AddEqn

LHS+x=RHS+x

3x=90

DivEqn

.LHS /3.=.RHS /3.

x=30

Having found the values of both variables, we can calculate the measure of each angle.

Angle	x=30	Measure
2x	2( 30)	60
90+x	90+ 30	120
90-x	90- 30	60

Let's summarize our findings. &x=30, y=90 &2x^(∘) = 60 &(y+x)^(∘) = 120 &(y-x)^(∘) = 60