DF bisects <EDG find FG the diagram is not to scale

Answer 1

Since we know that DF bisects angle EDG, we can conclude that the two resulting angles, angle EDF and angle FDG, are congruent.

Let's denote the measure of angle EDF as x. Since angle EDF and angle FDG are congruent, the measure of angle FDG is also x.

In triangle FGD, the sum of the angles is 180 degrees.
So, we have: x + x + angle FDG = 180 degrees.
Thus, 2x + x = 180 degrees.
Simplifying the equation, we get 3x = 180 degrees.
Dividing both sides by 3, we find that x = 60 degrees.

Since angle EDF is 60 degrees, angle FDG is also 60 degrees.

Now we can consider triangle FGD. In a triangle, the sum of the angles is 180 degrees.
Therefore, 60 degrees + 60 degrees + angle FGD = 180 degrees.
Simplifying this equation, we find that angle FGD = 180 degrees - 120 degrees = 60 degrees.

Since angle FGD is 60 degrees, and angle F is an exterior angle of triangle FGD, we know that angle F is supplementary to angle FGD.

So, angle F = 180 degrees - angle FGD = 180 degrees - 60 degrees = 120 degrees.

Therefore, we have found that angle F is 120 degrees.