DF bisects <EDG find FG. The diagram is not to scale

Question

EDG x+7 2x+4

Answer 1

To find FG, we need to find the length of DF and then subtract it from the length of DE.

Since DF bisects angle EDG, it splits the angle into two congruent angles. Let's call the measure of those congruent angles y.

Since the sum of the angles in a triangle is 180 degrees, we can set up the following equation:

x + 7 + 2x + 4 + y + y = 180

Simplifying the equation, we get:

3x + 11 + 2y = 180

Next, we need to find the measure of angle EDG. We can set up the following equation using the angle sum property:

x + 7 + 2x + 4 + y + y = 180

Simplifying the equation, we get:

3x + 11 + 2y = 180

Since DF bisects angle EDG, we know that the measure of angle EDG is equal to the measure of angle EDF, which is equal to 180 - 2y.

Now, we can set up the following proportion using the angle bisector theorem:

DF/DE = FG/EG

Since DF bisects angle EDG, we know that DF = DE, so the proportion becomes:

DF/DF = FG/EG

Simplifying the equation, we get:

1 = FG/EG

Since the length of DE is x + 7 + 2x + 4 = 3x + 11, we can substitute this value into our equation:

1 = FG/(3x + 11)

Now, we can solve for FG:

FG = 3x + 11

So, FG = 3x + 11.