27)
Opposite angles are equal.
x° angle is the opposite angle of the 90° angle.
Therefore, x°=90°.
28)
The 90° angle marked in the figure and the y° angles forms a linear pair.
Hence, both angles are supplementary. Supplementary angles sum upto 180°.
Therefore, we can write
[tex]\begin{gathered} y\degree+90\degree=180\degree \\ y\degree=180\degree-90\degree \\ y\degree=90\degree \end{gathered}[/tex]
Therefore, y°=90°.
29)
In the figure, let z°+46°=p°.
From figure, we can see that the p° angle is the opposite angle of y° angle.
Since opposite angles are equal, we can write
[tex]\begin{gathered} p\degree=y\degree \\ z\degree+46\degree=y\degree \end{gathered}[/tex]
Since from part 28, y°=90°, we get
[tex]\begin{gathered} z\degree+46\degree=90\degree \\ z\degree=90\degree-46\degree \\ z\degree=44\degree \end{gathered}[/tex]
Therefore, zh=44e.
30)
From figure,
[tex]\begin{gathered} w\degree=y\degree+90\degree+z\degree \\ \end{gathered}[/tex]
Substitute the known values.
[tex]\begin{gathered} w\degree=90\degree+90\degree+44\degree \\ w\degree=224\degree \end{gathered}[/tex]
Therefore, w°=224°
