Mathematics
Using ruler and compasses only, construct the quadrilateral ABCD in which ∠BAD = 45°, AD = AB = 6cm, BC = 3.6cm, CD = 5cm. Measure ∠BCD.
Answer
Steps of construction:
- Draw a line segment AB = 6 cm
- At A, construct ∠BAX = 45°.
- From AX, cut off AD = 6 cm.
- With B as centre and radius 3.6 cm, draw an arc.
- With D as centre and radius 5 cm, draw an arc to meet the previous arc at C.
- Join BC and DC. Then, ABCD is the required quadrilateral.
On measuring ∠BCD, it is 63°.
Hence, ∠BCD = 63°.
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