Question

In triangle ABC, if BD and CD bisect ∠B and ∠C , respectively, and ∠BDC = 135°, then find the measure of ∠BAC .
1. 90°
2. 45°
3. 65°
4. 75°

Answer 1

Correct Answer - Option 1 : 90°

Given:

∠BAC = 135°

Calculation:

∠DBC = ∠ABC/2 and ∠DCB = ∠ACB/2

In ΔBDC,

⇒ ∠BDC + ∠DBC + ∠DCB = 180°

⇒ ∠DBC + ∠DCB = 180° - 135° = 45°

⇒ ∠ABC/2 + ∠ACB/2 = 45°

⇒ ∠ABC + ∠ACB = 90°

In ΔABC,

⇒ ∠ABC + ∠ACB + ∠BAC = 180°

⇒ ∠BAC = 180° - 90° = 90°

∴ ∠BAC = 90°