Question

Which reason justifies the following statement?

If CEF is complementary to DCF, then DCF = FEG .

Answer 1

Answer; Complements of the same angle are congruent.

Answer 2

(A) Complements of the same angle are congruent.

Explanation:

Since, ∠CEF is complementary to ∠DCF, therefore

∠CEF+∠DCF=90° (1)

Also, ∠CEG=∠CEF+∠FEG

⇒90°=∠CEF+∠FEG (2)

Therefore, from(1) and (2), we get

∠CEF+∠DCF=90°

∠CEF+∠FEG=90°

Subtracting both the equations, we get

∠DCF-∠FEG=0

∠DCF=∠FEG.

Hence, ∠DCF≅∠FEG by the rule: Complements of the same angle are congruent.