Zara draws four rays from point O. The angles between consecutive rays are: angle AOB = 72°, angle BOC = 3x°, angle COD = 2x°, and angle DOA = 48°. All four angles together form a complete turn. What is the value of x?
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Worked Solution
Step 1: All four angles at point O form a complete turn.
Angle AOB + Angle BOC + Angle COD + Angle DOA = 360°
72° + 3x° + 2x° + 48° = 360°
Step 2: Collect like terms.
(72 + 48)° + (3x + 2x)° = 360°
120° + 5x° = 360°
Step 3: Solve.
5x° = 360° − 120° = 240°
x = 240 ÷ 5 = 48.
Check: 72 + 3(48) + 2(48) + 48 = 72 + 144 + 96 + 48 = 360°. ✓
Correct answer: 48
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