Constructing a quadrilateral when two adjacent sides and three angles are given
Construct a t...
Question
Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75° and DC || AB.
A
It is mandatory to give one more measurement.
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B
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C
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D
Trapezium cannot be constructed.
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Solution
The correct option is B Given, DC || AB.
Hence, ∠ABC+∠BCD=180 (Co-interior angles) ⇒75°+∠BCD=180° ⇒∠BCD=180°−75°=105° ⇒∠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.