In the figure, ABDE is a trapezium and BCDE is a rhombus. AFD is a straight line. AE // BD, ∠ADB=21∘\angle\text{ADB} = 21^\circ and ∠DBC=58∘\angle\text{DBC} = 58^\circ. Find ∠EFD\angle\text{EFD}. Ans: ___ ∘^\circ

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Worked solution

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1. Find $\angle\text{EBD}$ using the properties of a rhombus.

In the rhombus BCDEBCDE, the diagonal BDBD bisects the interior angle at BB.
∠EBD=∠DBC=58∘\angle\text{EBD} = \angle\text{DBC} = 58^\circ

2. Find $\angle\text{EFD}$ using the exterior angle theorem for $\triangle FBD$.

For △FBD\triangle FBD, ∠EFD\angle\text{EFD} is an exterior angle.
∠EFD=∠FBD+∠FDB\angle\text{EFD} = \angle\text{FBD} + \angle\text{FDB}
∠EFD=58∘+21∘=79∘\angle\text{EFD} = 58^\circ + 21^\circ = 79^\circ

Answer

7979

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