Problem 10 · 2020 Math Kangaroo
Easy
Geometry & Measurement
symmetry
In the figure, formed by a square and an equilateral triangle, the letters indicate the measures of the angles. Which of the following equalities is true?
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Answer: E — e + d = a
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Hint 1 of 2
The triangle is equilateral (all 60°) and the square has all 90° corners; mark what each labelled angle is built from.
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Hint 2 of 2
Track the angles along the slanted lines and look for the relation that always balances.
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Approach: chase angles using the 60° and 90° pieces
- The shape combines a square (90° corners) and an equilateral triangle (60° corners), so every labelled angle is a combination of these.
- Following the diagonal that splits the figure, the angles e and d on one side add up to the angle a on the other.
- Hence the true equality is e + d = a, choice E.
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