Exercise 5 Page 539

We want to find the values of x and y in the given parallelogram.

Let's recall the Parallelogram Opposite Sides Theorem, which tells us that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore, the lengths of the opposite sides are equal. 3x-10= x+2 and 6y-55= 15-y Let's solve the equations one at a time.

3x-10= x+2

SubEqn

LHS-x=RHS-x

2x-10=2

AddEqn

LHS+10=RHS+10

2x=12

DivEqn

.LHS /2.=.RHS /2.

x=6

We found that x=6. Let's now move on to the second equation.

6y-55= 15-y

AddEqn

LHS+y=RHS+y

7y-55=15

AddEqn

LHS+55=RHS+55

7y=70

DivEqn

.LHS /7.=.RHS /7.

y=10

We found that x=6 and y=10. This corresponds to answer B.