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. ${150}^o$
• D. ${125}^o$

Answer 1

The correct option is A ${70}^o$

Given,

$\angle ADB={30}^0$ and $\angle DCA={80}^0$.

Now,

$\angle DCA=\angle DBA={80}^0$ (Angle subtended by same chord are equal).

In $△ADB$,

$\angle ADB+\angle DBA+\angle DAB={180}^0$ (Sum of angles in triangle is ${180}^0$)

$⟹$ $\angle DAB={180}^0-{80}^0-{30}^0={70}^0$.

Hence, the measure of $\angle DAB$ is ${70}^0.$

Therefore, option $A$ is correct.