A straight angle measures 180 degrees.
Angle x and the 150-degree angle form a straight angle.
x + 150 = 180
x = 30
Angle z and the 100-degree angle form a straight angle.
z + 100 = 180
z = 80
Now you know the measures of two angles of the three angles of the triangle. The sum of the measures of the angle of a triangle equals 180 degrees.
x + y + z = 180
30 + y + 80 = 180
y + 110 = 180
y = 70
Answer: x = 30; y = 70; z = 80
