Problem: Side AB of triangle ABC has length 8 inches. Line DEF is drawn parallel to AB so that D is on segment AC and E is on segment BC. Line AE extended bisects angle FEC. If DE has length 5 inches, then the length of CE, in inches, is:
Answer Choices:
A. 451​
B. 13
C. 453​
D. 340​
E. 227​
Solution:
∠FEG=∠CEG. But ∠BAE=∠FEG, and ∠BEA=∠CEG. ∴∠BAE=∠BEA.∴BE=AB=8∴x8+x​=58​, x=340​.
