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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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