x=45
y=20
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!
