Question

In Triangle DEF, if angle D is congruent to angle E, DE= x + 4, EF= 4x - 8, and DF= 7X - 35 find X and the measure of each side

Answer 1

If angle D is congruent to angle E, then the triangle DFE is an isosceles triangle (look at the picture).

Therefore DF ≅ EF.

DE = x + 4, EF = 4x - 8, DF = 7x - 35

The equation:

7x - 35 = 4x - 8       add 35 to both sides

7x = 4x + 27       subtract 4x from both sides

3x = 27        divide both sides by 3

x = 9

DE = x + 4 → DE = 9 + 4 = 13

EF = 4x - 8 → EF = 4(9) - 8 = 36 - 8 = 28

DF = 7x - 35 → DF = 7(9) - 35 = 63 - 35 = 28

Answer:

x = 9, DE = 13, EF = 28, DF = 28.