Question

If the given figure, $\Delta ABC$ and $\Delta DBC$ are inscribed in a circle such that $\angle BAC={60}^{\circ }$ and $\angle DBC={50}^{\circ }$. Find $\angle BCD$.

• A. ${50}^{\circ }$
• B. ${80}^{\circ }$
• C. ${70}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

$\angle BAC=\angle BCD={60}^{\circ }$
As the angles in the same segments of a circle are equal.
In $\Delta BDC$,
$\angle BCD+\angle BDC+\angle DBC={180}^{\circ }$
$\angle BCD+{60}^{\circ }+{50}^{\circ }={180}^{\circ }$
$\angle BCD={70}^{\circ }$