Exercise 5 Page 499

Recall the Parallelogram Opposite Angles Theorem says that if a quadrilateral is a parallelogram, then its opposite sides are congruent.

x=4
y=8

Practice makes perfect

Let's find the value of each variable one at a time.

Value of x

Notice that the side of length 2x+3 and the side of length x+7 are opposite. Recall the Parallelogram Opposite Angles Theorem says that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore 2x+3= x+7. Let's solve it!

2x+3=x+7

SubEqn

LHS-x=RHS-x

x+3=7

SubEqn

LHS-3=RHS-3

x=4

Value of y

Notice that the side of length y+11 and the side of length 3y-5 are opposite. Recall the Parallelogram Opposite Angles Theorem says that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore y+11= 3y-5. Let's solve this equation, too.

y+11=3y-5

SubEqn

LHS-y=RHS-y

11=2y-5

AddEqn

LHS+5=RHS+5

16=2y

DivEqn

.LHS /2.=.RHS /2.

8=y

RearrangeEqn

Rearrange equation