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 â–³ 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 â–³ ZUY and â–³ 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
