So first of all is important to note that angle y and the 113° angle are what is known as corresponding angles. Basically, the sides that define them are parallel which means that they have the same measure. Then:
[tex]\measuredangle y=113^{\circ}[/tex]y and z are opposite angles. Just like before, one of the sides of y is parallel to one of the sides of z and the remaining sides are also parallel. Then they also have the same measure:
[tex]\measuredangle z=\measuredangle y=113^{\circ}[/tex]Using the same argument, x and the 113° have the same measure:
[tex]\measuredangle x=113^{\circ}[/tex]Finally, w and y are interior angles. This means that the sum of their measures must be equal to 180°. Then we get:
[tex]\measuredangle y+\measuredangle w=113^{\circ}+\measuredangle w=180^{\circ}[/tex]If we substract 113° from both sides of the last equality we get:
[tex]\begin{gathered} 113^{\circ}+\measuredangle w-113^{\circ}=180^{\circ}-113^{\circ} \\ \measuredangle w=67^{\circ} \end{gathered}[/tex]Then the answers are:
[tex]\begin{gathered} \measuredangle w=67^{\circ} \\ \measuredangle x=113^{\circ} \\ \measuredangle y=113^{\circ} \\ \measuredangle z=113^{\circ} \end{gathered}[/tex]