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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.

# Angles and Lines: Level 3 Challenges

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.

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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