Question

In the given figure, if $\angle$DAB = ${60}^{\circ },\angle ABD={50}^{\circ },$ then $\angle$ ACB is equal to:

• A. ${60}^{\circ }$
• B. ${50}^{\circ }$
• C. ${70}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

In $△$ ADB, we have

$\angle A+\angle B+\angle D={180}^{\circ }$

$\Rightarrow {60}^{\circ }+{50}^{\circ }+\angle D={180}^{\circ }$

$\Rightarrow \angle D={180}^{\circ }–{110}^{\circ }={70}^{\circ }$

i.e., $\angle ADB={70}^{\circ }$

Now, $\angle ACB=\angle ADB={70}^{\circ }[\because$ Angles in the same segment of a circle are equal]

Hence, (c) is the correct answer.