Question

In the given figure, it is given that chords $AB=PQ,\angle AOB={55}^0,$ and $\angle POQ=x^0$, find $x$.

• A. 25
• B. 45
• C. 55
• D. 35

Answer 1

The correct option is C

55

Here, we are given that $AB=PQ$

Now, let us consider $\Delta AOB$ and $\Delta POQ$,

Here, $AB=PQ$ [given]

$AO=PO=$ radius of the circle

Similarly, $BO=QO=$ radius of the circle

$\therefore \Delta AOB\cong \Delta POQ$ [By SSS congruency]

Hence, $\angle POQ=\angle AOB={55}^{\circ }$ [C.P.C.T]