Learn how to find the measure of an angle by subtracting using the figure below. However, first you need to know how to find the measure of those that are already given.

Let m = measure of.

Notice the angle measures for ∠TYZ, ∠SYZ,and ∠XYZ

m∠TYZ = 30°

m∠SYZ = 120°

m∠XYZ = 180°

Now find m∠SYT, m∠XYT, and m∠XYS

To find the angle measures above, you need to make some good observations.

To find m∠SYT, notice that m∠SYT + m∠TYZ = m∠SYZ

m∠SYT + 30 = 120

m∠SYT + 30 - 30 = 120 - 30

m∠SYT = 90

To find m∠XYT, notice that m∠XYT + m∠TYZ = m∠XYZ

m∠XYT + 30 = 180

m∠XYT + 30 - 30 = 180 - 30

m∠XYT = 150

To find m∠XYS, notice that m∠XYS + m∠SYT = m∠XYT

m∠XYS + 90 = 150

m∠XYS + 90 - 90 = 150 - 90

m∠XYS = 60