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Outside the Box Geometry

# Angle Hunting

The hypotenuses of the 7 right triangles shown above are all on the same line. What is the measure of the angle marked $$x$$?

These three quizzes introduce geometry through interesting topics and challenging puzzles. This course contains many of each of these types of problems:

• Angle Hunting: using the axioms for angle-geometry to figure out the value of an unknown angle

• Strategic Geometry: going beyond the basic skills to solve complex problems and to master more challenging techniques and proofs

• Beautiful Explorations: diving deeply into areas of geometry where the elegance and beauty speaks for itself

What is the measure of the green angle, $$\angle A?$$

Find the measure of the red angle marked $$x$$ below.

Hint: Try sliding two lines; shifting a line (without rotating it) doesn’t change the angle of its intersection with other lines.

What can we say about the base angles of any isosceles triangle?

If these three segments are connected end-to-end to form a triangle, will the triangle be acute, right, or obtuse?

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