Question

If chords AB and PQ are equal, $\angle AOB={55}^{\circ }$, and $\angle POQ=x,$ then find the value of $x$.

• A. 55${}^{\circ }$
• B. 25${}^{\circ }$
• C. 50${}^{\circ }$
• D. 45${}^{\circ }$

Answer 1

The correct option is A 55${}^{\circ }$

Given,
$AB=PQ$
Using the property, equal chords subtend equal angles at the centre, we have,
$\Rightarrow \angle AOB=\angle POQ$
$\Rightarrow \angle AOB={55}^{\circ }$
$\therefore \angle POQ=x={55}^{\circ }$