Exercise 13 Page 616

Let's mark the congruent corresponding parts in our triangles. Note that the naming of the triangles can help us in this regard: △ D E F≅ △ Q R S D and Q are corresponding vertices, as are E and R and F and S.

Examining the triangles, we see that ∠ F and ∠ S are congruent corresponding angles. Thus, to find x we need to know ∠ F. Using the Triangle Sum Theorem, we can write an equation to determine ∠ F: 29^(∘)+123^(∘)+m∠ F=180^(∘) Let's solve this equation.

29^(∘)+123^(∘)+m∠ F=180^(∘)

AddTerms

Add terms

152^(∘)+m∠ F=180^(∘)

SubEqn

LHS-152^(∘)=RHS-152^(∘)

m∠ F=28^(∘)

When we know the measure of ∠ F we can equate this with the measure of ∠ S and solve for x.

2x^(∘)+2^(∘)=28^(∘)

SubEqn

LHS-2^(∘)=RHS-2^(∘)

2x^(∘)=26^(∘)

DivEqn

.LHS /2.=.RHS /2.

x^(∘)=13^(∘)

To find the value of y, we equate the expression for DE, (5y-7), with it's congruent corresponding side in △ QRS which is known.

5y-7=38

AddEqn

LHS+7=RHS+7

5y=45

DivEqn

.LHS /5.=.RHS /5.

y=9