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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.

(The radius of the wedges are each 1 unit, and the diameter is the circle is 2 units.)

\(\overline{BC}\) and \(\overline{DE}\) are parallel lines.

The green angle is \( 50 ^ \circ \) and the purple angle is \( 8 0 ^ \circ \).

What is the red angle ( \(\angle DAE\) ) in degrees?

The image on the left shows how hexagons could be used to cover the plane without gaps or overlaps.

Can copies of the purple region on the right be arranged to cover the plane without gaps or overlaps?

The two vertical lines are perfectly parallel. What is the sum of the three blue angles?

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