Question

In ∠DEF, if ∠D ≅ ∠E, DE = x + 4, EF = 4x - 8, and DF = 7x - 35, find x and the measure of each side.

A) x = 5, DE = 9, EF = 12, DF = 14
B) x = 7, DE = 11, EF = 20, DF = 28
C) x = 10, DE = 14, EF = 32, DF = 45
D) x = 12, DE = 18, EF = 40, DF = 55

Answer 1

To find x and the measure of each side in ∠DEF, set up an equation using the given lengths of DE, EF, and DF. Solve the equation to find x, and then substitute the value back into the original equations to find the measure of each side.

Step-by-step explanation:

To find x and the measure of each side in ∠DEF, we can use the fact that ∠D ≅ ∠E. We can set up an equation using the given lengths of DE, EF, and DF:

DE = x + 4

EF = 4x - 8

DF = 7x - 35

Since ∠D ≅ ∠E, we also know that DE = EF:

x + 4 = 4x - 8

Solving this equation, we find that x = 12.

Substituting this value back into the original equations, we can find the measure of each side:

DE = 12 + 4 = 16

EF = 4(12) - 8 = 40 - 8 = 32

DF = 7(12) - 35 = 84 - 35 = 49

Therefore, the correct option is D) x = 12, DE = 16, EF = 32, DF = 49.