Question

What is the value of $\angle DBC$ in the above figure?

• A. ${20}^{\circ }$
• B. ${100}^{\circ }$
• C. ${60}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

Since the angle subtended by an arc at the centre of a circle is double the angle subtended by it at any remaining point of the circle,
$\angle AOB=2\times \angle ACB$
$\Rightarrow \angle ACB=\frac{1}{2}\times \angle AOB=\frac{1}{2}\times {40}^{\circ }={20}^{\circ }$
Using angle sum property in $△BDC,$
$\angle DBC+\angle BCD+\angle CDB={180}^{\circ }.$
$⟹\angle DBC={180}^{\circ }-{20}^{\circ }-{100}^{\circ }$
$={60}^{\circ }$