91Ó°ÊÓ

The given diagram is:

The two angles are said to be congruent angles if they have equal measure.

If two angles $A$and $B$are congruent then it can be written as $∠Aâ‰\dots ∠B$.

The theorem 2-3 states that the vertical angles are congruent.

From the diagram it can be noticed that:

The angles $ZOY$and $UOV$are vertically opposite angles.

Therefore, from the theorem 2-3, it can be said that the angles $ZOY$and $UOV$are congruent angles.

Therefore, $∠ZOYâ‰\dots ∠UOV$.

As, $∠ZOYâ‰\dots ∠UOV$, therefore, $∠ZOY=∠UOV$

Therefore, $∠ZOY=∠UOV=35°$.

Therefore, the measure of the angle $ZOY$is $35°$.

From the given diagram it can be noticed that:

$∠ZOW=∠ZOY+∠YOW$

Therefore,

$$\begin{gathered} ∠ZOW=∠ZOY+∠YOW \\ =35°+120° \\ =155° \end{gathered}$$

Therefore, the measure of the angle $ZOW$is $155°$.