Question

AF is the angle bisector of the angle $\angle EAD$. If AE = EF and $\angle AEF={120}^{\circ }$, the value of $\angle EAD$ is .

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${15}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

As AF is the angle bisector of $\angle EAD$,
$2\times \angle EAF=\angle EAD$.
Also, $AE=EF$. Hence, $△AEF$ is an isosceles triangle. Therefore, $\angle EAF=\angle EFA$.

Now, the sum of all three angles of a triangle is ${180}^{\circ }$.
$\Rightarrow \angle EAF+\angle EFA+\angle AEF={180}^{\circ }\Rightarrow 2\angle EAF+\angle AEF={180}^{\circ }\Rightarrow 2\angle EAF+{120}^{\circ }={180}^{\circ }\Rightarrow 2\angle EAF={180}^{\circ }-{120}^{\circ }\Rightarrow 2\angle EAF={60}^{\circ }\therefore \angle EAD={60}^{\circ }$
So, the correct answer is ${60}^{\circ }$