Question

Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75° and DC || AB.

• A. Trapezium cannot be constructed.
• B.
• C. It is mandatory to give one more measurement.
• D.

Answer 1

The correct option is B

Given, DC || AB.
Hence,
$\angle ABC+\angle BCD=180$ (Co-interior angles)
$\Rightarrow 75°+\angle BCD=180°$
$\Rightarrow \angle BCD=180°-75°=105°$
$\Rightarrow \angle BCD=105°$.

Steps of Construction:

1. Draw a line segment AB of length 6cm.
2. Construct an angle of 75° at the point B and extend the line.
3. Keeping B as the centre, cut an arc of radius 4cm on the extended line. Mark the point to be C.
4. Construct 105° at the point C and extend the lines.
5. Keeping C as the centre, cut an arc of radius 3.2cm on the extended line. Mark the point to be D.
6. Join D to A and C and C to B.

Trapezium ABCD is hence constructed.