Question

Find values of x and y for which ABCD must be a parallelogram. The diagram is not drawn to scale.

Answer 1

ANSWER
$x=4, y=8$

EXPLANATION

If ABCD is a parallelogram, then

line AB is parallel to line DC .

This means that,

$(x + 2) \degree$
and

$(2x - 2) \degree$
are alternating angles.

Alternate angles are congruent.

This implies that,

$2x - 2 = x + 2$

We group like terms to obtain,

$2x - x = 2 + 2$

This simplifies to,

$x = 4$

Also, if ABCD is a parallelogram then,

BC is parallel to AD. This means that,

$5y - 8 = y + 24$

We group like terms to get,

$5y - y = 24 + 8$

This simplifies to,

$4y = 32$

We divide both side by 4 to get,

$y = 8$

Answer 2

2x-2 = x+2
2x-x = 2+2
x = 4

5y-8 = y+24
5y-y = 24+8
4y = 32
y = 8