Answer:
Explanation:
Problem 12:
I think that (2x-y)+60=(2x+y)+40
Because of the Alternate Interior Angles theorem, which places the 40 next to (2x+y) so then you know they are a linear pair. Same can be done for the side with the 60 degree angle. So both sides add up to 180 so they are congruent themselves and you can put them in this format:
(2x-y)+60=(2x+y)+40
-40 -40
We do this to remove the 40 from the right side completely, and whatever you do to one side of the equation you have to do to the other as well so remove 40 from both.
(2x-y)+20=(2x+y)
-2x -2x
Again, we are just trying to find out y right now
-y +20=y
+y +y
20 = 2y
10 = y
Then insert the y into an equation telling us that it is equal to 180 (because we know that from before) to get what x is
(2x-y)+60=180
We can also input our y that we found out was 10 from before:
(2x-10)+60=180
And now we can add up 60 and -10
2x+50=180
Now subtract 50 to both sides
2x=130
And divide both sides by 2
x=75
So x=75 and y=10
Feel free to ask any questions
Problem 13:
The same type of working out, just with different numbers