Problem 12 · 2009 Math Kangaroo
Stretch
Geometry & Measurement
symmetry
In the triangle shown, one interior angle measures 68°. The three angle bisectors of the triangle are drawn. What is the size of the angle marked with a question mark?
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Answer: B — 124°
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Hint 1 of 2
The three bisectors meet at the incenter; the marked angle is one of the angles there.
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Hint 2 of 2
The incenter angle facing a vertex equals 90° plus half that vertex's angle.
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Approach: use the incenter angle formula
- The bisectors meet at the incenter, and the marked angle faces the 68° vertex.
- The two bisectors meeting there come from the other vertices B and C; that angle is 90° + (A/2).
- With A = 68°, the marked angle = 90° + 34° = 124°.
Mark:
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