Question

In the given figure, $ABCD$ is a cyclic quadrilateral in which $\angle CAD={25}^o$, $\angle ABC={50}^o$ and $\angle ACB={35}^o$. Then $\angle DAB$ is:

• A. $\angle DAB={70}^o$
• B. $\angle DAB={130}^o$
• C. $\angle DAB={50}^o$
• D. $\angle DAB={120}^o$

Answer 1

The correct option is D $\angle DAB={120}^o$

Given-$ABCD$ is a cyclic quadrilateral. $AC$ is its diagonal. $\angle CAD={25}^o,$ $\angle ABC={50}^o,$ and $\angle ACB={35}^o.$

To find: $\angle DAB$

In $\Delta ABC,$ we have,

by angle sum property,

$\angle ABC+\angle BCA+\angle CAB={180}^o$

$⟹$ $\angle CAB={180}^o-(\angle ABC+\angle ACB)$
$={180}^o-({35}^o+{50}^o)={95}^o.$

$\therefore \angle DAB=(\angle CAB+\angle CAD)={95}^o+{25}^o={120}^o$.

Hence, option $D$ is correct.