Question

2 points
BD and CD are angle bisectors of angles ABC and ACP respectively. if
angle BDC-44 then value of angle BAC is
A
D
P
O 68
088
O Bo
O
112​

Answer 1

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=

2

1

∠A

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