2026 · Q72
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: ABCD is a quadrilateral in which AD = BC. What is ∠ABC + ∠ADC equal to?
Statement IAB is parallel to DC.
Statement IIAD is not parallel to BC.
Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsQuadrilaterals and Polygons
- AThe Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
With AB‖DC and AD=BC, ABCD could be an isosceles trapezium (giving ∠ABC+∠ADC=180°) or a parallelogram (opposite angles equal, sum undetermined) — so statement I alone does not suffice, and statement II alone says nothing. Together they force a non-parallelogram trapezium with equal legs, i.e. an isosceles trapezium, where ∠ABC+∠ADC=180°. Both statements together are needed, option C.