Ahmad is sawing a wooden plank along straight line PQ. At point O on the plank, he makes two saw cuts creating rays OA and OB on the same side of PQ. The exterior angle of triangle OAB at vertex B measures 117°, and angle BAO = 45°. Ahmad also notices that angle POA is exactly 3 times angle BOQ. What is angle BOQ?
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Worked Solution
Step 1: Find angle AOB using the exterior angle theorem.
The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
Exterior angle at B = angle BAO + angle AOB
117° = 45° + angle AOB
angle AOB = 72°
Step 2: Set up the straight-line angle equation.
Let angle BOQ = x. Then angle POA = 3x.
All three angles along straight line PQ sum to 180°:
3x + 72° + x = 180°
4x = 108°
x = 27°
Answer: angle BOQ = 27°.
Correct answer: 27°
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