Question

In the figure(not drawn to scale), $ADF$ and $BEF$ are triangles and $EC$ $=$ $ED$, find $y$.

• A. ${90}^o$
• B. ${91}^o$
• C. ${92}^o$
• D. ${93}^o$

Answer 1

The correct option is A ${90}^o$

In a $\Delta CDE$, we have

$EC=ED$

$\Rightarrow \angle EDC=\angle ECD={28}^{\circ }$ .....Angles opposite to equal sides are also equal

$\Rightarrow \angle ACB=\angle ECD={28}^{\circ }$ .....Vertically opposite angles In a $\Delta ABC$

We know $\angle y=\angle ACB+{62}^{\circ }$ .....Exterior angle property of triangle $ABC$

$\Rightarrow \angle y={28}^{\circ }+{62}^{\circ }$

$\Rightarrow \angle y={90}^{\circ }$