Question

The given figure represents a kite. Find the value of x.

Answer 1

It represents a kite whose diagonals are perpendicular to each other

Now, in $△AEB$

$\angle ABE+{90}^o+{60}^o={180}^o\Rightarrow \angle ABE={30}^o$

Also , since it is a kite so $△ABC\simeq △ADC$

Hence, $\angle ACB=\angle ACD={20}^o$

Now, in $△BEC$

$\angle EBC+{90}^o+{20}^o={180}^o\Rightarrow \angle EBC={70}^o$

So, $\angle x={20}^o+{70}^o$