The sum of all the angles in a triangle is 180°.
There is a right angle -> a 90° angle on the hypotenuse of the largest triangle (the largest being the one that contains both smaller triangles)
To solve this problem, you don't really need to solve y.
Next to the 48° angle, you have two of the same angles, both x variables.
The sum of these three angles has to be 180°[tex]48 + 2x = 180 \\ 2x = 180 - 48 \\ 2x = 132 \\ x = 66[/tex]
Now that we have x, we can calculate the value of z.
We add the value of x and the 90° angle, we later subtract it from 180°
Calculating the value of z:
[tex]66 + 90 = 156 \\ 180 - 156 = 24 \\ z = 24[/tex]
If you really want to know the value of y, you just add up the 90° angle and the 48°, then subtract that from 180°
[tex]90 + 48 = 138 \\ 180 - 138 = 42 \\ y = 42[/tex]
