An angle at a bend between parallel lines
An angle at a bend between parallel lines
IP 1
7 marks
In the diagram, \(AB\) is parallel to \(ED\). The point \(C\) lies between the parallel lines, on the same side of \(BD\) as \(A\) and \(E\). \(\angle ABC=38^\circ\) and \(\angle CDE=47^\circ\).
- Find \(\angle BCD\), giving a reason for each step.[2]
- Prove that \(\angle BCD=\angle ABC+\angle CDE\) for every such position of \(C\).[2]
- Now a point \(K\) lies between the parallel lines on the other side of \(BD\), away from \(A\) and \(E\). Find and prove the relationship between \(\angle ABK\), \(\angle BKD\) and \(\angle KDE\), where \(\angle BKD\) is the angle less than \(180^\circ\).[3]
Solution:
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Answer:(a) \(85^\circ\) (b) alternate angles with \(CX\parallel AB\parallel ED\) give \(\angle BCD=\angle ABC+\angle CDE\) (c) \(\angle ABK+\angle BKD+\angle KDE=360^\circ\), by interior angles with \(KY\parallel AB\parallel ED\)
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