Circles — Maths STD 9 — Question

3. 70°.

Solution:

In $\triangle\text{ADB},$ we have

$\angle\text{A}+\angle\text{B}+\angle\text{D}=180^\circ$ [Angle sum property of a triangle]

$\Rightarrow60^\circ+50^\circ+\angle\text{D}=180^\circ$

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

i.e., $\angle\text{ABD}=70^\circ$

Now, $\angle\text{ACB}=\angle\text{ADB}=70^\circ$

[$\because$ Angles in the same segment of a circle are equal]

Hence, (c) is the correct answer.