Question

If $\angle COD={80}^{\circ },$ then $\angle CAD$ = ___.

• A. $\angle CBD$
• B. ${40}^{\circ }$
• C. ${160}^{\circ }$
• D. $\angle COB$

Answer 1

Answer: (A), (B)

The correct options are
A $\angle CBD$
B ${40}^{\circ }$

Since the angle subtended by an arc at the centre of a circle is double the angle subtended by it at any remaining point on the circle, we have
$\angle COD=2\times \angle CAD.$
Also, $\angle COD=2\times \angle CBD.$
Thus, $\angle CAD=\angle CBD=\frac{{80}^{\circ }}{2}={40}^{\circ }.$