Question

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Answer 1

Given:

The triangle ABC is given.

To find:

a) The angle FED.

b) The complementary angle of the angle CBD.

Step-by-step explanation:

a) Using the angle sum property of the triangle FED,

`\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}`

So, the angle FED becomes,

`\begin{gathered} \angle FED=16x-8 \\ =16(8)-8 \\ =128-8 \\ \angle FED=120^(\circ) \end{gathered}`

b) Next let us find the angle CBD.

`\begin{gathered} \angle CBD=-2x+81 \\ =-2(8)+81 \\ =-16+81 \\ \angle CBD=65^(\circ) \end{gathered}`

Finding the angle EDF,

`\begin{gathered} \angle EDF=2x+9 \\ =2(8)+9 \\ =16+9 \\ =25^(\circ) \end{gathered}`

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,

`\begin{equation*} \angle FED=120^(\circ) \end{equation*}`

b) Angle CBD and EDF are complementary angles.