Question

5. In the adjoining figure, BE and CE are bisectors of ABC and ZACD respectively. If BEC = 25°, then BAC is equal to :
D
a. 50°
b. 253
C. 65°
d. 12°​

Answer 1

Answer:

Extend the line BC to E

BD and CD are angular bisectors,

∴∠ABD=∠DBC=x and ∠ACD=∠DCE=y

∠ABC=2x and ∠ACE=2y

Consider △ABC,

∠ACE=∠ABC+∠BAC ------exterior angle is equal to sum of interior opposite angle

2y=2x+∠A

y−x=2∠A------(i)

Consider △BCD,

∠DCE=∠DBC+∠BDC ------exterior angle is equal to sum of interior opposite angle

y=x+∠D

y−x=∠D------(ii)

From(i) and (ii)

∠D=21 ∠A

Option A. Rest are not true.