Three rays from point O divide the full angle at O into three parts: angle AOB = 2n°, angle BOC = (3n + 10)° and angle COA = (n + 50)°. Find the value of n.
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Worked Solution
Step 1: Angles at a point sum to 360°.
Step 2: Write the equation: 2n + (3n + 10) + (n + 50) = 360.
Step 3: Collect n-terms: 2n + 3n + n = 6n.
Collect constants: 10 + 50 = 60.
Simplified: 6n + 60 = 360.
Step 4: Isolate 6n: 6n = 360 − 60 = 300.
Step 5: Solve: n = 300 ÷ 6 = 50.
Verify: 2(50) + (3×50+10) + (50+50) = 100 + 160 + 100 = 360°. ✓
Answer: 50
Correct answer: 50
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