Question P6 Angle chasing
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A landscaper installs a triangular trellis EAD in a garden bed, with a parallelogram lattice panel BCDE fitted inside it; B lies on the trellis edge AD. The posts AB and BE are equal in length. Given angle DBC = 46° and angle BCD = 70°, find angle EAB.
Answer
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One angle gives you the next, until you reach the angle asked for.
In this one. The parallelogram carries the angle at D across to B, and that angle is the exterior angle of the isosceles triangle — so the angle at A is simply half of it.
A figure has several angles marked with only one or two values given, and words like 'isosceles', 'parallel', or 'straight line' point to which rule to use first.
Children apply an angle rule to the wrong triangle or the wrong straight line in a crowded figure, or stop one step before the angle actually asked for.
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