Question

Construct a trapezium ABCD in which AB || DC, ∠A = 105°, AD = 3 cm, AB = 4 cm and CD = 8 cm.

Answer 1

We know that,

∠A + ∠D = 180°   ...[Sum of adjacent angle of a trapezium is 180°]

105° + ∠D = 180°

∠D = 180° – 105°

∠D = 75°

Steps of construction:

Step I: Draw AB = 4 cm.

Step II: Draw ${\displaystyle \overline{AX}}$ that is ∠BAX = 105°.

Step III: Mark a point D on AX that is AD = 3 cm.

Step IV: Draw ${\displaystyle \overline{DY}}$ that is ∠ADY = 75°.

Step V: Mark a point C that is CD = 8 cm.

Step VI: Join BC.

Hence, ABCD is the required trapezium.