Question

Find the measure of angle y in the figure which is at the centre of the circle

• A. ${99}^{\circ }$
• B. ${105}^{\circ }$
• C. ${90}^{\circ }$
• D. ${109}^{\circ }$

Answer 1

The correct option is D ${109}^{\circ }$

Given a circle with center at P.Let AB and CD be the chords of the circle which are produced to meet at E. AC and BD intersect at O
Now, $\angle BAC=18$, $\angle AEC=35$
In $triangleCAE$
Sum of angles $=180$
$\angle CAE+\angle ACE+\angle AEC=180$
$18+35+\angle ACE=180$
$\angle ACE={127}^{\circ }$
$\angle ACD=180-\angle ACE=180-127={53}^{\circ }$ (Linear pair)
$\angle CDB=\angle CAB={18}^{\circ }$ (Angles in same segment)
Now, In $△ODC$
Sum of angles $=180$
$\angle ODC+\angle OCD+\angle COD=180$
$18+53+y=180$
$y={109}^{\circ }$