Question

ABCD is a cyclic quadrilateral such that $\angle ADB={30}^{o}and\angle DCA={80}^o$, then $\angle DAB=$

• A. ${70}^o$
• B. ${100}^o$
• C. ${125}^o$
• D. ${150}^o$

Answer 1

The correct option is A

${70}^o$

ABCD is a cyclic quadrilateral. $\angle DCA={80}^{o}and\angle ADB={30}^o$

$\because \angle ADB=\angle ACB$ (Angles in the same segment)

$\therefore \angle ACB={30}^o$

$\therefore \angle BCD={80}^o+{30}^o={110}^o$

$\because$ ABCD is a cyclic quadrilateral

$\therefore \angle BAD+BCD={180}^o$

$\Rightarrow \angle BAD+{110}^o={180}^o$

$\Rightarrow BAD={180}^o-{110}^o={70}^o$

$\therefore \angle DAB={70}^o$