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# Geometry Warmups

Mathematics is filled with shapes that are kaleidoscopic in variety. Wielded since ancient times, the power of geometry helps us examine and measure these shapes.

# Geometry Warmups: Level 1 Challenges

$1^2 + 1^2 + 1^2 + 3^2 + 4^2 + 7^2 + 11^2 = \, ?$

If lines $$l$$ and $$m$$ are parallel, then what is the value of angle $$x$$ (in degrees)?

The diagram above shows a large square, whose midpoints are connected up to form a smaller square. We then connect up the midpoints of the smaller square, to obtain the inner shaded square.

What fraction of the large square is shaded?

The picture above is a semicircle with diameter $$\overline{AC},$$ and $$\overline{AC}$$ is perpendicular to $$\overline{BD}.$$ It is known that $$AB=4\text{ cm}$$ and $$BC=1\text{ cm}.$$ If $$BD=x,$$ find $$x.$$

The clock shown has hands positioned at 5 o'clock. What is the degree measure of angle $$x$$?

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