Exercise 113 Page 60

We are given a diagram and asked to find the values of x and y. Examining the given diagram, we see that y and 119^(∘) form a linear pair. By the Linear Pair Postulate we know that these angles are supplementary. This means their measures sum to 180^(∘). y+119^(∘)=180^(∘) By solving the equation we can determine the measure of y.

y+119^(∘)=180^(∘)

SubEqn

LHS-119^(∘)=RHS-119^(∘)

y=61^(∘)

Let's add this to the diagram. Also, notice that (5x+11)^(∘) and 61^(∘) are corresponding angles. Since the two lines cut by the third line are parallel, we know by the Corresponding Angles Theorem that these angles are congruent. Let's add this information as well.

Since they are congruent, we can equate their measures. 5x+11^(∘)=61^(∘) By solving this equation we can determine the value of x.

5x+11^(∘)=61^(∘)

SubEqn

LHS-11^(∘)=RHS-11^(∘)

5x=50^(∘)

DivEqn

.LHS /5.=.RHS /5.

x=10^(∘)