I am given triangle EDF with angles E and F being congruent. What is the perimeter of the triangle if ED= 2x+8, EF= 3x-6, and DF= 4x-6.

since angles E and F are congruent, the sides opposite them (DF and DE) are congruent. That means that

4x-6 = 2x+8
x = 7

Now you can figure the perimeter.

To find the perimeter of the triangle EDF, we need to add up the lengths of all three sides.

First, we're given that angles E and F are congruent, which means they have the same measure. Since the triangle is not equilateral, we know that angles D, E, and F are all different angles.

Since angles E and F are congruent, we can set up an equation to find their measure:
E = F

Now, let's set up an equation to find the value of x:
2x + 8 = 3x - 6

To find x, we can subtract 2x from both sides of the equation:
8 = x - 6

Then, add 6 to both sides of the equation:
14 = x

Now that we know the value of x, we can substitute it back into the given lengths of the sides:

ED = 2x + 8 = 2(14) + 8 = 28 + 8 = 36
EF = 3x - 6 = 3(14) - 6 = 42 - 6 = 36
DF = 4x - 6 = 4(14) - 6 = 56 - 6 = 50

Now, we can calculate the perimeter by adding up the lengths of all three sides:

Perimeter = ED + EF + DF
= 36 + 36 + 50
= <<36+36+50=122>>122

Therefore, the perimeter of triangle EDF is 122 units.