Question

In the given figure ABC and ADE are triangles such that AB = AD, AE = EC . Find the measure of angle DAE

• A. ${10}^{\circ }$
• B. ${20}^{\circ }$
• C. ${25}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

Answer: (B)

${20}^{\circ }$

We know that the angles opposite to the sides will also have the same relation.

In triangle ABC, since $AB=AD$
$=>\angle ADB=\angle ABD$
Now, since sum of angles in a triangle ABC $={180}^o$
$\angle ABD+\angle ABD+{20}^0={180}^o$
$=>2\angle ABD={160}^o$
$=>\angle ABD={80}^o$
In triangle AEC, since $AE=EC$
$=>\angle EAC={30}^0$
Now, since sum of angles in a triangle ABC $={180}^o$
$\angle ABC+\angle BAC+{30}^0={180}^o$
$\angle ABD+\angle BAC+{30}^0={180}^o$
${80}^o+\angle BAC+{30}^0={180}^o$
$=>\angle BAC={70}^o$
$=>\angle BAD+\angle DAE+\angle EAC={70}^o$
$=>{20}^0+\angle DAE+{30}^0={70}^o$
$=>\angle DAE={20}^o$.