Question

Find the values of x and y for which the quadrilateral below must be a parallelogram.

Answer 1

A quadrilateral will be a parallelogram when:
$7x+7=21$ and $(2y-1)^{\circ}=49^{\circ}$

So let's solve these equations in order to find $x$ and $y$:
$7x+7=21$
$7x=21-7$
$7x=14$
$x=14/7=2$

$2y-1=49$
$2y=49+1$
$2y=50$
$y=50/2=25$

Solution: $x=2$ and $y=25$

Answer 2

Since there is no picture, find here-under the conditions that a quadrilateral becomes a parallelogram:
( All are either or)
1- opposite sides should be congruent
2- opposite angles should be congruent
3- opposite sides parallel
4-The sum of 2 adjacent angles to equal 180°
5 the 2 diagonals intersect in their middle

With any of these conditions, if confirmed, you can conclude that the quadrilateral is a parallelogram (By the way a rectangle is a parallelogram with one angle =90°