Constructing a Trapezium When Its Two Sides and Two Angles Are Given
Question 186C...
Question
Question 186
Construct a trapezium ABCD in which AB∥DC,∠A=105∘, AD = 3 cm, AB = 4 cm and CD = 8 cm.
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Solution
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.