In ΔABC, ∠B = 68° and ∠C = 32°. Sides AB and AC are produced to points D and E, respectively. The bisectors of ∠DBC and ∠BCE meet at F. What is the measure of ∠BFC?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 50°.
From the angle bisector property -
∠BFC = 90° - ∠A/2
In triangle ABC -
∠A + ∠B + ∠C = 180°
⇒ ∠A = 180° - 32° - 68°
⇒ ∠A = 80°
So,
∠BFC = 90° - 80°/2
⇒ ∠BFC = 90° - 40°
⇒ ∠BFC = 50°