Question

The value of $x$ in the gi ven figure is

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

Answer 1

The correct option is C

${30}^{\circ }$

Since $△ABC$ is equilateral, we must have $\angle A=\angle B=\angle C={60}^{\circ }$

[In any equilateral triangle, all angles are ${60}^{\circ }$]
$\therefore \angle ACD={120}^{\circ }$ [$\because \angle BCA$ and $\angle ACD$ form linear pair]
$△ACD$ is isosceles [$\because$ AC=CD, as shown in the figure]
$⟹\angle CAD=\angle ADC=x^{\circ }$ (If two sides of a triangle are equal, the angles opposite these sides are also equal)
In $△ACD$, by angle sum property, wee must have

$x^{\circ }+x^{\circ }+{120}^{\circ }={180}^{\circ }$

$⟹x^{\circ }=\frac{({180}^{\circ }-{120}^{\circ })}{2}={30}^{\circ }$