In the figure, OA, OB, OC and OD are four rays from point O. Angle AOB = angle COD = 35°. Angle BOC = 2 × angle AOB. Angle DOA (going the remaining way round) completes the full turn. What is the size of angle DOA (the reflex path)?
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Worked Solution
Step 1: Angle BOC = 2 × angle AOB = 2 × 35° = 70°.
Step 2: Sum of known angles = angle AOB + angle BOC + angle COD = 35° + 70° + 35° = 140°.
Step 3: Reflex angle DOA = 360° − 140° = 220°.
Check: 35 + 70 + 35 + 220 = 360. ✓
Correct answer: 220°
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