Question

The value of $x^{\circ }$ in the given figure is _______

• A. ${60}^{\circ }$
  
• B. ${45}^{\circ }$
  
• C. ${30}^{\circ }$
  
• D. ${15}^{\circ }$

Answer 1

The correct option is C

${30}^{\circ }$

(i)$△ABC$ is equilateral (all angles are equal)
(ii)$\therefore \angle ACD={120}^{\circ }$ (exterior angle)
(iii)$△ACD$ is isosceles $(AC=CD)$
(iv)$\angle CAD=\angle ADC=x^{\circ }$ (Base angles of an isosceles)
(v)$\therefore x=\frac{(180-120)}{2}={30}^{\circ }$ Hence (c)