Question

In the given figure, ABC is isosceles triangle with $AB=AC,\angle BCD={20}^{\circ }.$ The measure of $\angle ACB$ is equal to

• A.
  ${100}^{\circ }$
• B.
  ${80}^{\circ }$
• C.
  ${60}^{\circ }$
• D.
  ${70}^{\circ }$

Answer 1

The correct option is D

${70}^{\circ }$
$AB=AC\left(Given\right)\angle BCD={20}^{\circ }\left(Given\right)In\Delta DEC,\text{by Angle sum property}\angle ADC+\angle DEC+\angle BCD={180}^{\circ }\Rightarrow \angle ADC+{90}^{\circ }+{20}^{\circ }={180}^{\circ }(\because \angle DEC={90}^{\circ }and\angle BCD={20}^{\circ })\Rightarrow \angle ADC={70}^{\circ }\text{Now, angles subtended by a chord}\text{in the same segment are equal.}$

$therefore\angle ABC=\angle ADC={70}^{\circ }Also,\angle ACB=\angle ABC(\because AB=AC)\therefore \angle ACB={70}^{\circ }$

Hence, the correct answer is option (d).