Question

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

• A. $x={110}^{\circ }$ $y={225}^{\circ }$
• B. $x={110}^{\circ }$ $y={125}^{\circ }$
• C. $x={100}^{\circ }$ $y={125}^{\circ }$
• D. $x={100}^{\circ }$ $y={120}^{\circ }$

Answer 1

The correct option is B

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

$y={125}^{\circ }$

$\text{In}\Delta OBC$,

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

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

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

Now in cyclic quadrilateral, ABCD

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

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