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Find x in the given figure.

The quadrilateral ABCD in the given figure is cyclic because each of its four vertices A, B, C, and D lie on the circle's circumference.

We know that the sum of either pair of opposite angles of a cyclic quadrilateral is 180^o.

$\therefore \angle A+\angle C={180}^o$

$\Rightarrow (2x+{40}^o)+(4x-{64}^o)={180}^o$

$\Rightarrow 6x-{24}^o={180}^o$

$\Rightarrow 6x={204}^o$

$\Rightarrow \mathit{x}\mathbf{=}{\mathbf{34}}^{\mathbf{o}}$