Question

$\text{In the figure below,}\Delta ABC\text{is an}\text{equilateral triangle and EC = CD. What}\text{is the measure of}\angle EDC?$

• A. ${60}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D

${30}^{\circ }$

$\text{Since}\Delta ABC\text{is equilateral,}\angle ABC=\angle ACB=\angle CAB={60}^{\circ }.$

$\text{By exterior angle property in}△CDE,\angle ACB=\angle CED+\angle EDC\dots \left(1\right)$

$\text{Since CE = CD,}△CDE\text{is isosceles.}$

$\text{Angles opposite to equal sides are}\text{equal in an isosceles triangle.}$
$\Rightarrow \angle CED=\angle EDC$

$\text{Substituting in equation (1), we get}\angle ACB=2\angle EDC\Rightarrow {60}^{\circ }=2\angle EDC\Rightarrow \angle EDC=\frac{{60}^{\circ }}{2}\Rightarrow \angle EDC={30}^{\circ }$