Question

In the given figure, if O is the centre of the circle, then find the measure of $\angle OCD+\angle ODC.$

• A. ${100}^{\circ }$
• B. ${110}^{\circ }$
• C. ${120}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is A ${100}^{\circ }$

Given that AB and CD are equal chords, $\angle AOB=\angle COD.$
[Equal chords of a circle subtend equal angles at the centre.)

By anlge sum property of a triangle, $\angle AOB={80}^{\circ }$
$\Rightarrow \angle COD={80}^{\circ }$
$\Rightarrow \angle OCD+\angle ODC={180}^{\circ }-{80}^{\circ }={100}^{\circ }$ Angle sum property of a triangle)