Question

Complete.

6. Find the values of y and z.

Short answer

The values of y and z are 50 and 60 respectively.

Step-by-step solution

Step 1. Label the given diagram.

The labelled diagram is:

Step 2. Description of step.

From the given diagram it can be noticed that the lines AB and CD are parallel to each other.

From the given diagram it can be noticed that the angles$\angle EFG$ and$\angle FGH$ are alternate interior angles.

Therefore,$\angle EFG=\angle FGH$

Therefore, it can be noticed that:

$\begin{array}{c}\angle EFG=\angle FGH\\ y=50\end{array}$

Therefore, the value of y is 50.

From the given diagram it can be noticed that the angles$\angle EOF$ and$\angle GOH$ are vertically opposite angles.

Therefore, $\angle EOF=\angle GOH$.

Therefore, it can be obtained that:

$\begin{array}{c}\angle EOF=\angle GOH\\ =z\end{array}$

By using the exterior angle theorem it can be noticed that:

$$\begin{gathered} \angle EOF+\angle EFO=110 \\ z+y=110 \\ z+50=110 \\ z=110-50 \\ z=60 \end{gathered}$$

Therefore, the value of z is 60.

Step 3. Write the complete statement.

The values of y and z are 50 and 60 respectively.