Find angle measures
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