MCQ
In the given figure, $\triangle\text{ABC}$ and $\triangle\text{DBC}$ are inscribed in a circle such that $\angle\text{BAC}=60^\circ$ and $\angle\text{DBC}=50^\circ.$ Then, $\angle\text{BCD}=?$ 
- A$60^\circ$
- B$50^\circ$
- C$80^\circ$
- ✓$70^\circ$
✓
Answer
Correct option: D.
$70^\circ$
$\angle\text{BDC}=\angle\text{BAC}=60^\circ$ (Angles in the same segment of a circle)
In $\triangle\text{BDC},$ we have
$\angle\text{DBC}+\angle\text{BDC}+\angle\text{BCD}=180^\circ$ (Angle sum property of a triangle)
$\therefore50^\circ+60^\circ+\angle\text{BCD}=180^\circ$
$\Rightarrow\angle\text{BCD}=180^\circ-(50^\circ+60^\circ)=(180^\circ-110^\circ)=70^\circ$
$\Rightarrow\angle\text{BCD}=70^\circ$
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