Question

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

• A. 55${}^{\circ }$
• B. 25${}^{\circ }$
• C. 35${}^{\circ }$
• D. 45${}^{\circ }$

Answer 1

The correct option is A

55${}^{\circ }$

Given, AB = PQ.
Since equal chords subtend equal angles at the centre, we have
$\angle AOB=\angle POQ.$
$\angle AOB={55}^{\circ }⟹\angle x=\angle POQ={55}^{\circ }$