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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 2 Challenges


What is the sum of the 6 blue angles?

What is the measure of the blue angle in degrees?

In the figure above, four line segments \(AB, CD, EF, GH\) intersect at a single point. Find the value (in degrees) of the angle sum \(x + y + w + z.\)

Note: \(\angle EFH = 55 ^ \circ\), \(\angle ACD = 37 ^ \circ\), and \(\angle GHF = 85 ^ \circ\).

Is it possible to cut this obtuse triangle into pieces so that every piece is an acute triangle?

My failures so far ...

If \(\overline{AB}\) is parallel to \(\overline{DE}\), then what is the measure of angle \(BCD\) in degrees?


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