Question

Find the value of x and the value of y.

Answer 1

x = 45

y = 20

Step-by-step explanation:

3y + 6y + 2x + 90 = 360 (Angles of a parallelogram ALWAYS add up to 360)

9y + 2x + 90 = 360 (Combine like terms) (2x = 90 because angles are congruent) {2x = 90; x = 45]

9y + 90 + 90 = 360 (Add like terms)

9y + 180 = 360 (Subtract 180 from both sides)

9y = 180 (Divide both sides)

y = 20

Answer 2

Answer:
x=45
y=20

Step-by-step explanation:
The first thing we want to do is create 2 equations (since there are 2 variables) paying attention to three important pieces of information:
1) those two lines on the shape are parallel
2) the line segment on the right form a right angle at the bottom corner
3) In a quadrilateral, all of the angles add up to 360 degrees

Let A be the left side of the shape
Let B be the right side of the shape
Let C be the bottom side of the shape
(These are just for the explanation to be more clear)

Using 2), we know that line C is perpendicular to line B. But because line A is parallel to line B, line C is also perpendicular to line A. And this means that 2x degrees = 90 degrees.
Boom! First equation found.

2x=90

Using 3), we can say that all the angles of this shape will add up to 360 degrees since this shape is a quadrilateral.
Boom! Second equation found.

3y+6y+2x+90=360

Here are the equations:
3y+6y+2x+90=360
2x=90

There are a number of strategies we can use to solve for x and y (ex. First solving for x and substituting it to the other equation, etc.) but for this question, we can plug the second equation directly into the first by subbing in 90 as 2x.

3y+6y+2x+90=360
-> 3y+6y+90+90=360

And now, we solve for y.
3y+6y+90+90=360
9y+180=360
Subtract both sides by 180
9y=360-180
9y=180
Divide both sides by 9
y=20

Now that we found y, we only need the second equation to find x.

2x=90
Divide both sides by 2
x=45

Therefore, the value of x is 45 and the value of y is 20.

I hope this helps!