Question

1. in each figure, for what values of x and y is the figure a parallelogram? see example 3

a.
3x + 6
y + 2
2y - 3
4 - x
b.
(4x - 12)°
(5y - 6)°
(3y + 46)°
(3x + 5)°

Explanation:

Part a

Step1: Set opposite sides equal

$3x + 6 = 4 - x$

Step2: Solve for x

$3x + x = 4 - 6$
$4x = -2$
$x = \frac{-2}{4} = -\frac{1}{2}$

Step3: Set other opposite sides equal

$y + 2 = 2y - 3$

Step4: Solve for y

$2 + 3 = 2y - y$
$y = 5$

Part b

Step1: Set opposite angles equal

$4x - 12 = 3x + 5$

Step2: Solve for x

$4x - 3x = 5 + 12$
$x = 17$

Step3: Set other opposite angles equal

$5y - 6 = 3y + 46$

Step4: Solve for y

$5y - 3y = 46 + 6$
$2y = 52$
$y = 26$

Answer:

a. $x = -\frac{1}{2}$, $y = 5$
b. $x = 17$, $y = 26$