Question

In the given figure, chords AB and CD are equal. if $\angle OCD=60°$ and $\angle AOB=70°$, then $\angle ODC=$ .

• A. 40°
• B. 60°
• C. 70°
• D. 50°

Answer 1

The correct option is D 50°

Given that AB = CD,
$\angle OCD=60°$ and $\angle AOB=70°.$
In the given figure AB and CD are the equal chords.
We know that, equal chords subtend equal angles at the center.
$\therefore \angle AOB=\angle COD={70}^{\circ }$
In $△OCD$
$\angle OCD+\angle COD+\angle ODC=180°$ ..... (Angle sum property)
60° + 70° + $\angle ODC$ = 180°
$\angle ODC=180°-(60°+70°)=50°$
Hence, $\angle ODC=50°$