Question

In the given figure, O is the centre of the circle and $\angle ABC={55}^{\circ }$. Calculate the values of x and y.

Answer 1

$\text{In}\Delta OBC$,

Ext. $\angle AOC=\angle OBC+\angle BCO$

$={55}^{\circ }+{55}^{\circ }={110}^{\circ }$

$\therefore x={110}^{\circ }$

Now in cyclic quadrilateral, ABCD

$\angle ADC+\angle ABC={180}^{\circ }\Rightarrow y+{55}^{\circ }={180}^{\circ }$

$\therefore y={180}^{\circ }-{55}^{\circ }={125}^{\circ }$