Answer:
The image below will be used to explain the question
From the image above,
We will have the following relationships
[tex]\begin{gathered} \angle\text{BCD}=\angle CDF(alternate\text{ angles ar equal)} \\ \angle\text{BCD}=35^0 \\ \angle CDF=x \end{gathered}[/tex]
With the relation above, we can conclude that
[tex]x=33^0[/tex]
Hence,
The value of x = 33°
Step 2:
The following relation below will be used to calculate the value of y
[tex]\begin{gathered} \angle CBD=\angle BDE(alternate\text{ angles are equal)} \\ \angle CBD=109^0 \\ \end{gathered}[/tex]
By applying this, we will conclude that
[tex]\angle BDE=109^0[/tex]
The relation below will be helpful to get the exact value of y
[tex]\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}[/tex]
By substituting the values, we will have
[tex]\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}[/tex]
Hence,
The value of y= 38°
The relation below will be used to figure out the value of z
[tex]\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}[/tex]
Hence,
the value of z= 109°
