Given:
The triangle ABC is given.
To find:
a) The angle FED.
b) The complementary angle of the angle CBD.
Explanation:
a) Using the angle sum property of the triangle FED,
[tex]\begin{gathered} \angle FED+\angle EDF+\angle DFE=180 \\ 16x-8+2x+9+35=180 \\ 18x+36=180 \\ 18x=180-36 \\ 18x=144 \\ x=8 \end{gathered}[/tex]
So, the angle FED becomes,
[tex]\begin{gathered} \angle FED=16x-8 \\ =16(8)-8 \\ =128-8 \\ \angle FED=120^{\circ} \end{gathered}[/tex]
b) Next let us find the angle CBD.
[tex]\begin{gathered} \angle CBD=-2x+81 \\ =-2(8)+81 \\ =-16+81 \\ \angle CBD=65^{\circ} \end{gathered}[/tex]
Finding the angle EDF,
[tex]\begin{gathered} \angle EDF=2x+9 \\ =2(8)+9 \\ =16+9 \\ =25^{\circ} \end{gathered}[/tex]
Since the sum of the angles CBD and EDF are 90 degrees.
So, angle CBD and EDF are complementary angles.
Final answer:
a) The angle is,
[tex]\begin{equation*} \angle FED=120^{\circ} \end{equation*}[/tex]
b) Angle CBD and EDF are complementary angles.
