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a) As BCEF is a rhombus, this means that all of its sides are equal. ∴ △CBF = △CEF

b) As BCEF is a rhombus, BC = BF. ∴△CBF and △CEF are isosceles △s

∠BCF = ∠ECF = ∠EFC = 51°
∠FEC = 180° – ∠ECF – ∠EFC
= 180° – 51° – 51°
= 78°

c) ∠BCD = 360° – 51° – 51° – 147°
= 111°

∠CDA = 180° – ∠BCD (Angles between parallel lines)
= 180° – 111°
= 69°

∠BDC = ∠CDA – ∠BDA
= 69° – 32°
= 37°

 

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