Find the value of x and y for which the quadrilateral is a parallelogram. Show your solution and explain. (Need the answers today pls)

Question

Answer 1

Hello Beaux;

Parallelogram; all neighboring adjent angle pairs are supplemetary, add up to 180.

So, 140 + 4y = 180 ==> 4y = 40 ==> y = 10°.

40 + 2x + 2 = 180 ==> 2x = 138 ==> x = 69°.

Answer 2

There are a couple of different ways you could go about this:

The first way: set opposite angles equal to each other, because in a parallelogram, opposite angles are congruent:

So to solve for x, you could say 2x + 2 = 140.

Subtract 2 from both sides to end up with 2x = 138.

Lastly, divide both sides by 2 to end up with your answer of x = 69.

Solve for y the same way...4y = 40. Divide both sides by 4 and end up with an answer of y = 10.

The second way: set consecutive angles = 180, because in a parallelogram, consecutive angles are supplementary.

So your equations to solve would be 140 + 4y = 180, and 40 + 2x + 2 = 180.

You will get the same answer either way - so pick which method is best for you!