Two straight lines AB and CD intersect at point O. Angle AOC = 3x° and angle BOC = (x + 40)°. Find angle AOD.
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Worked Solution
Step 1: Angles AOC and BOC lie on straight line AB, so they sum to 180°.
3x + (x + 40) = 180
4x + 40 = 180
Step 2: Solve for x.
4x = 140
x = 35
Step 3: Find angle AOC.
AOC = 3(35) = 105°
Step 4: Find angle AOD.
AOC and AOD lie on straight line CD, so AOC + AOD = 180°.
AOD = 180 − 105 = 75°
Check (vertically opposite): BOC = (35 + 40)° = 75° = AOD ✓
Answer: 75°
Answer: 75°
Correct answer: 75°
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