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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. See more

Level 3


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.

In the figure above, 3 unit squares are placed side by side. Find the sum of the angle measurements \(a,\) \(b,\) and \(c,\) in degrees.

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).

Lines \(l\) and \(m\) are parallel. \(M\), \(N\) and \(O\) are points such that \(M\) is on \(l\) and \(N\) is on \(m\) and \(O\) is between the two lines. If the smaller angle between \(l\) and \(MO\) is \(35^{\circ}\) and \(\angle MON = 105^{\circ}\), find the acute angle between \(m\) and \(NO\).


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