Question

Find the value of x and y in which each quadrilateral mist be a parallelogram.

Answer 1

Recall the property of parallelograms that tell us that the diagonals intercept producing equal segments in each of them. Then, as the diagonals intercept in the midpoint of each diagonal, then we can create the following equations and solve them one at a time (making the measure of one segment equal the value on the other half of the diagonal):

5 y - 4 = 36 then we solve here for y

add 4 to both sides

5 y = 36 + 4

5 y = 40

divide both sides by 5

y = 40 / 5

y = 8

Now the second equation:

4 x - 10 = 18

add 10 on both sides

4 x = 28

divide both sides by 4 to isolate x

x = 28 / 4

x = 7