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# Angles and Lines

Forgive us for being obtuse, but this is a cute concept, and we think it’s right for you.

Determine the value of \(x\).

\(ABC\) is a right triangle with \(\angle C=90^\circ\). \( M\) is the midpoint of \(AB,\) and \(D\) is a point such that \(MC = MD\) with points \(C\) and \(D\) lying on opposite sides of \(AB,\) as shown in the diagram.

If \( \angle DAB = 40 ^ \circ\), what is \( \angle DCA \)?

In a quadrilateral \(ABCD\), \(\angle ABD = \angle BCA = \angle CDB = \angle DAC = 30^\circ\).

Find the smaller of the two angles (in degrees) between the diagonals AC and BD.

\(\)

**Note:** The image might not be necessarily up to scale.

Find \(x\) (in degrees).

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