Problem 13 · 2019 Math Kangaroo
Hard
Geometry & Measurement
symmetry
The vertices of a square ABCD are labelled anti-clockwise. A and C are the vertices of an equilateral triangle AEC, whose vertices are also labelled anti-clockwise. How big is the angle CBE?
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Answer: C — 135°
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Hint 1 of 2
Place the square on coordinates and find the equilateral triangle's apex E on the correct (anticlockwise) side.
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Hint 2 of 2
Measure angle CBE from the coordinates.
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Approach: coordinates and angle measurement
- Take A(0,0), B(1,0), C(1,1), D(0,1). The anticlockwise triangle AEC puts E outside the square beyond AC.
- Triangle BCE is isosceles, and the apex angle at B works out to 135°.
- So angle CBE = 135°.
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