Question

In the given figure, the value of $a$ is:

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (B)

${40}^{\circ }$

$ABCD$ is a cyclic quadrilateral.
Thus, $\angle D+\angle B={180}^o$ ...[Opposite angles of cyclic quadrilateral are supplementary]
$⟹$ $130+\angle B=180$
$⟹$ $\angle B={50}^{\circ }$.

And, $AB$ is a diameter, hence, $\angle ACB={90}^o$ (Angle in a semi circle)
Thus, In $△ABC$,
$\angle ABC+\angle ACB+\angle CAB={180}^o$ ...[Angle sum property]
$⟹$ ${50}^o+{90}^o+\angle CAB={180}^o$
$⟹$ $\angle CAB={40}^{\circ }$.

Hence, option $B$ is correct.