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 <em>add 35 to both sides</em>
7x = 4x + 27 <em>subtract 4x from both sides</em>
3x = 27 <em>divide both sides by 3</em>
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
<h3>Answer:</h3><h3>x = 9, DE = 13, EF = 28, DF = 28.</h3>