Problem 7 · 2015 Math Kangaroo
Medium
Geometry & Measurement
careful-counting
A quadrilateral is called convex if all its internal angles are less than 180°. The number of right angles in a convex quadrilateral is n. Which of the following lists is a complete listing of all possible values of n?
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Answer: B — 0, 1, 2, 4
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Hint 1 of 2
Could a convex quadrilateral have exactly three right angles?
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Hint 2 of 2
The four interior angles must add to 360°.
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Approach: use that the four angles sum to 360°
- 0, 1 and 2 right angles are all possible (e.g. a general quadrilateral, a kite, a right trapezoid).
- If three angles were 90°, the fourth would also be 360−270 = 90°, giving four — so exactly three is impossible.
- Four right angles is a rectangle, which works, so the complete list is 0, 1, 2, 4 (B).
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