Question

Assertion: ABCD is a trapezium if ∠A + ∠C = 180°.

Reason: If one pair of opposite sides of a quadrilateral are parallel then it is a trapezium.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is false but R is true.

Explanation:

Assertion:

• In a trapezium, only one pair of opposite sides is parallel.
• ∠A + ∠C = 180° can happen in some quadrilaterals that are not trapeziums.
• Also, this condition is only true if A and C are interior angles on the same side of a transversal between parallel lines not just any opposite angles.

Reason:

• This is correct by definition of a trapezium or trapezoid.