In trapezium ABCD, AB is parallel to CD. Given that ∠ADC = 68° and ∠BCD = 75°, find ∠DAB and ∠ABC.
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Worked Solution
Step 1: AB ∥ CD with transversal AD. ∠DAB and ∠ADC are co-interior angles.
∠DAB = 180° − 68° = 112°
Step 2: AB ∥ CD with transversal BC. ∠ABC and ∠BCD are co-interior angles.
∠ABC = 180° − 75° = 105°
Step 3: Verify — angle sum of quadrilateral ABCD:
112° + 105° + 75° + 68° = 360° ✓
Answer: ∠DAB = 112° and ∠ABC = 105°
Correct answer: 112° and 105°
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