we know that
If two triangles are similar, then their corresponding angles are congruent
In this problem
we have that
First case
angle x and angle 60 are corresponding angles
angle (x+10) and angle (2x-50) are corresponding angles
so
x=60
x+10=2x-50
2x-x=10+50
x=60
is ok
Second case
angle (x+10) and angle 60 are corresponding angles
angle x and angle (2x-50) are corresponding angles
so
x+10=60
x=50
x=2x-50
2x-x=50
x=50
therefore
