Exercise 21 Page 532

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

Value of x

The angles that measure 2x + 41 and 115 are opposite angles. Recall the Theorem 6.4, which tells us that if a quadrilateral is a parallelogram, then its opposite angles are congruent. Therefore, the measures of these angles are equal. 2x + 41= 115 Let's solve above equation to find the value of x.

2x + 41 = 115

SubEqn

LHS-41=RHS-41

2x = 74

DivEqn

.LHS /2.=.RHS /2.

x = 37

Value of y

The sides with lengths 2y + 19 and 3y + 13 are opposite sides in our parallelogram. Recall the Theorem 6.3, 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. 2y + 19= 3y + 13 Let's solve above equation to find the value of y.

2y + 19 = 3y + 13

SubEqn

LHS-19=RHS-19

2y = 3y - 6

SubEqn

LHS-3y=RHS-3y

- y = - 6

MultEqn

LHS * (- 1)=RHS* (- 1)

y = 6