In trapezium ABCD, AB is parallel to DC. Angle DAB = 116° and Angle BCD = Angle ADC − 20°. Find Angle BCD.
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Worked Solution
Step 1: AB is parallel to DC, so co-interior angles on the same side sum to 180°.
Angle DAB + Angle ADC = 180°
116° + Angle ADC = 180°
Angle ADC = 64°
Step 2: Use the given relationship.
Angle BCD = Angle ADC − 20°
Angle BCD = 64° − 20° = 44°
Step 3: Verify using the angle sum of a quadrilateral.
Angle ABC = 180° − 44° = 136° (co-interior, AB ∥ DC)
Sum = 116° + 64° + 44° + 136° = 360° ✓
Correct answer: 44°
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