Question

Find the values of the variables x , y and z in the parallelogram

Answer 1

The image below will be used to explain the question

From the image above,

We will have the following relationships

`\begin{gathered} \angle\text{BCD}=\angle CDF(alternate\text{ angles ar equal)} \\ \angle\text{BCD}=35^0 \\ \angle CDF=x \end{gathered}`

With the relation above, we can conclude that

`x=33^0`

Hence,

The value of x = 33°

Step 2:

The following relation below will be used to calculate the value of y

`\begin{gathered} \angle CBD=\angle BDE(alternate\text{ angles are equal)} \\ \angle CBD=109^0 \\ \end{gathered}`

By applying this, we will conclude that

`\angle BDE=109^0`

The relation below will be helpful to get the exact value of y

`\begin{gathered} \angle BDE+\angle CDF+\angle CDB=180^0(SUM\text{ OF ANGLES ON A STRAIGHT LINE)} \\ \angle BDE=109^0 \\ \angle CDF=x=33^0 \\ \angle CDB=y \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \angle BDE+\angle CDF+\angle CDB=180^0 \\ 109^0+33+y=1180^0 \\ 142^2+y=180^0 \\ y=180-142 \\ y=38^0 \end{gathered}`

Hence,

The value of y= 38°

The relation below will be used to figure out the value of z

`\begin{gathered} \angle BDE=\angle CFD(correspond\in g\text{ angles are equal)} \\ \angle BDE=109^0 \\ \angle CFD=z \\ z=109^0 \end{gathered}`

Hence,

the value of z= 109°