Calculate the angle $X$ and angle $Y$ value in the given figure?

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Solution

Determine the unknown angles.
The figure has two equal adjacent sides.
So, the figure is a kite.
The diagonals of the kite bisect the angles of the kite.
Since $AD$ is diagonal, it bisects the angles $∠ BDC and ∠ BAC$ .
Find the value of $X$ :
$\begin{array}{rcl} ∠ CAD & = & ∠ BAD \\ \Rightarrow & X = 37 ° \end{array}$
Find the value of $Y$ :
$\begin{array}{rcl} ∠ CDA & = & ∠ BDA \\ \Rightarrow & Y = 70 ° \end{array}$
Value of angle $X$ and angle $Y$ are $37 ° and 70 °$ respectively

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