Question

How to solve for 27-30 (X, Y, Z, and W)

Answer 1

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

`\begin{gathered} y\degree+90\degree=180\degree \\ y\degree=180\degree-90\degree \\ y\degree=90\degree \end{gathered}`

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

`\begin{gathered} p\degree=y\degree \\ z\degree+46\degree=y\degree \end{gathered}`

Since from part 28, y°=90°, we get

`\begin{gathered} z\degree+46\degree=90\degree \\ z\degree=90\degree-46\degree \\ z\degree=44\degree \end{gathered}`

Therefore, zh=44e.

30)

From figure,

`\begin{gathered} w\degree=y\degree+90\degree+z\degree \\ \end{gathered}`

Substitute the known values.

`\begin{gathered} w\degree=90\degree+90\degree+44\degree \\ w\degree=224\degree \end{gathered}`

Therefore, w°=224°