Question

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

choices are;

A. x = 10; y = 38
B. x = 10; y = 21
C. x = 10; y = 7
D. x = 7; y = 10

Answer 1

with any parallelogarm, the diagonal bisect each other, so basically, the diagonals cut each other in half

so, this means
4y - 7 = y + 14

and

4x -2 = x + 28

hope this helps

Answer 2

The correct option is C.

Explanation:

The diagonals of a parallelogram bisect each other.

The intersection point of both diagonals divides the diagonal AC in two equal parts.

`4x-2=x+28`

`4x-x=2+28`

`3x=30`

`x=10`

The value of x is 10.

The intersection point of both diagonals divides the diagonal BD in two equal parts.

`4y-7=y+14`

`4y-y=7+14`

`3y=21`

`y=7`

The value of y is 7.

Therefore the correct option is C.