Question

If in the given figure, triangle ABC and triangle DCE are equilateral, the measure of the angle ACD is

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

Answer 1

The correct option is D

${60}^{\circ }$

Given triangle ABC and triangle DCE are equilateral.

Then $\angle ABC=\angle BAC=\angle ACB=\angle DCE=\angle CED=\angle CDE={60}^{\circ }$

[In any equilateral triangle, all angles are ${60}^{\circ }$]

Now, $\angle BCA+\angle ACD+\angle DCE={180}^{\circ }$

$⟹{60}^{\circ }+\angle ACD+{60}^{\circ }={180}^{\circ }$

$⟹\angle ACD={60}^{\circ }$