Question

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

Show your work please! :)

Answer 1

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

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

Answer 2

ANSWER

`x=4, y=8`

Step-by-step 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`