Notice that ZY=ZW.
This means that triangle △ ZYW is isosceles, so angles ∠ ZWY and ∠ ZYW are congruent.
We can add the two angle measures given on the figure to find the measure of the angle at Z.
m∠ YZW=45+55=100
We can use the Triangle Angle Sum Theorem in triangle △ ZYW to find the measure of these two congruent angles.
This result also gives that m∠ Y=40.
Let's put these measures on the figure.
We can now use the Triangle Angle Sum Theorem in triangles △ ZUY and △ ZUW to find the measure of the angles we are asked to compare.
m∠ ZUY+45+40=180 &⟹ m∠ ZUY=95
m∠ ZUW+55+40=180 &⟹ m∠ ZUW=85
We are now ready to write the inequality we were asked to find.
95>85
⇓
m∠ ZUY> m∠ ZUW
