Question

In a quadrilateral ABCD, ∠A + ∠B = 180°. ∴ It is a ______.

Options

• Parallelogram

• Rectangle

• Trapezium

• Kite

Answer 1

In a quadrilateral ABCD, ∠A + ∠B = 180°. ∴ It is a trapezium.

Explanation:

Step 1: Analyze the given condition

In any quadrilateral, if the sum of a pair of consecutive angles is 180°, it means that the two sides forming those angles are parallel.

Given that ∠A + ∠B = 180°, the sides AD and BC must be parallel to each other.

Step 2: Define the quadrilateral types

• A parallelogram is a quadrilateral with two pairs of parallel sides.
• A rectangle is a type of parallelogram where all angles are 90°.
• A trapezium or trapezoid is a quadrilateral with at least one pair of parallel sides.
• A kite is a quadrilateral with two distinct pairs of equal-length adjacent sides.

Step 3: Conclude the classification

The given condition only guarantees one pair of parallel sides AD and BC. This property aligns directly with the definition of a trapezium. While a parallelogram also has this property, the condition is not sufficient to prove that the other pair of sides AB and CD are also parallel.

Therefore, the most accurate and general classification is a trapezium.