Question 186 Construct a trapezium ABCD in which AB∥DC,∠A=105∘, AD = 3 cm, AB = 4 cm and CD = 8 cm.
We know that. ∠A+∠D=180 [∵ sum of adjacent angle of a trapezium is 180∘] 105∘+∠D=180∘ ∠D=75∘
Steps of Construction Step I Draw AB = 4 cm. Step II Draw ¯AX such that ∠BAX=105∘. Step III Mark a point D on AX such that AD = 3 cm. Step IV Draw ¯DY such that ∠ADY=75∘. Step V Mark a point C such that CD = 8 cm. Step VI Join BC. Hence, ABCD is the required trapezium.