Question

In the given figure, $\angle ADC$ is?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

Answer: (B)

${60}^{\circ }$

Let the line from $A$ cuts $BC$ at $E$.

Then, $\angle AEB={60}^{\circ }$
$\angle AEB+\angle AEC={180}^{\circ }$
${60}^{\circ }+\angle AEC={180}^{\circ }$
$\angle AEC={120}^{\circ }$
In quadrilateral $AECD$, we have

$\angle DAE=\angle ECD={90}^{\circ }$
$\angle DAE+\angle ECD+\angle AEC+\angle ADC={360}^{\circ }$
$\angle ADC=360-300$
$\angle ADC={60}^{\circ }$