Points A, O and B lie on a straight line. Ray OD is drawn from O such that angle AOD = 4y°. Ray OC bisects angle AOD. Given that angle DOB = (y + 30)°, find angle AOC.
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Worked Solution
Step 1: Use the angles-on-a-straight-line property.
Angle AOD + angle DOB = 180°
4y + (y + 30) = 180
5y + 30 = 180
5y = 150
y = 30
Step 2: Find angle AOD.
Angle AOD = 4 × 30 = 120°
Step 3: OC bisects angle AOD, so angle AOC = angle AOD ÷ 2.
Angle AOC = 120° ÷ 2 = 60°
Answer: 60°
Correct answer: 60°
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