ABC is a triangle. The bisectors of theinternal angle B and external angle C intersect at D. if BDC = 60^ then A is

ABC is a triangle. The bisectors of theinternal angle B and exter…

MCQ

$ABC$ is a triangle. The bisectors of theinternal angle $\angle B$ and external angle $\angle C$ intersect at $D$. if $\angle BDC = 60^\circ$ then $\angle A$ is

A
$120^\circ$
B
$180^\circ$
✓
$60^\circ$
D
$150^\circ$

✓

Answer

Correct option: C.

$60^\circ$

Consider $△ABC$ Let $BC$ be extended to $E$ Since Angular bisectors Meet at $D \angle ABD = \angle DBC ⋯ (1)$
$\angle ACD =\angle DCE ⋯ (2)$
Consider $△DBC$ By External sum property $\angle DCE = \angle BDC + \angle DBC $
$⟹ 2 \angle DCE = 2(60^\circ ) + 2 \angle DBC $
$⟹ \angle ACE = 120^\circ +\angle ABC $
By external sum property of
$△ABC \angle ACE = \angle BAC + \angle ABC$
$⟹ \angle A = 60^\circ$

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