MCQ
In $\triangle\text{ABC}$ it is given that $\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}.$ If $\angle\text{B}=70^\circ$ and $\angle\text{C}=50^\circ$ then $\angle\text{BAD}=?$
- ✓$30^\circ$
- B$40^\circ$
- C$45^\circ$
- D$50^\circ$
✓
Answer
Correct option: A.
$30^\circ$
in $\triangle\text{ABC}$ it is given that $\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}.$
$\Rightarrow AD$ bisects $\angle\text{BAC}$
In $\triangle\text{ABC},$
$\angle\text{BAC}+\angle\text{ABC}+\angle\text{ACB}=180^\circ$
$\Rightarrow\angle\text{BAC}+70^\circ+50^\circ=180^\circ$
$\Rightarrow\angle\text{BAC}=60^\circ$
$\Rightarrow\angle\text{BAD}=\angle\text{DAC}=30^\circ$
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