Given:
∠JEK + ∠DFH = 90°
Find:
relationship, if any, of ∠JEK to angles CFL, HFG, LFE
Solution:
We note that ∠DFG = 90° = ∠DFH + ∠HFG, so ∠JEK ≅∠HFG.
We also note that ∠HFG and ∠CFL are vertical angles, so ∠JEK ≅∠CFL.
And ∠LFE and ∠DFH are vertical angles, so ∠JEK + ∠LFE = 90°.
Evaluating the choices, we find
A) false. The angles are not complementary, they are equal.
B) false. The angles are not equal, they are complementary.
C) false. The angles are not supplementary, they are equal.
D) TRUE. The angles are equal.
The appropriate choice is ...
D) ∠JEK ≅∠CFL