Exercise 4 Page 499

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

x=11
y=14

Practice makes perfect

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

Value of x

Notice that the angles measuring 8x-8 and 6x+14 are consecutive angles. Recall that the Parallelogram Opposite Angles Theorem says that if a quadrilateral is a parallelogram, then its opposite angles are congruent. Therefore 8x-8= 6x+14. Let's solve it!

8x-8=6x+14

SubEqn

LHS-6x=RHS-6x

2x-8=14

AddEqn

LHS+8=RHS+8

2x=22

DivEqn

.LHS /2.=.RHS /2.

x=11

Value of y

Notice that the angles measuring 6y+16 and 7y+2 are consecutive angles. Recall the Parallelogram Opposite Angles Theorem says that if a quadrilateral is a parallelogram, then its opposite angles are congruent. Therefore 6y+16= 7y+2. Let's solve this equation.

6y+16=7y+2

SubEqn

LHS-6y=RHS-6y

16=y+2

SubEqn

LHS-2=RHS-2

14=y

RearrangeEqn

Rearrange equation

y=14