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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.

Let \(P\) be an interior point of triangle \(ABC\).

Let \(Q\) and \(R\) be the reflections of \(P\) in \(AB\) and \(AC\), respectively.

If \(QAR\) is a straight line, find \(\angle BAC\) in degrees.

The image is not drawn to scale.

Find \(x\) (in degrees).

**acute** angle between \(m\) and \(NO\).

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