Question

In the figure not drawn to scale, ABCD is a trapezium and AB // DC. ∠CBF = 70°, ∠ADC = 108°. AB = AE. Find ∠BCD.

Answer 1

in triangle AEB,

AE=AB

hence the angles opposite to this lines are equal

angle AEB = angel ABE

angle ABE =angle  EFd (alternative angles)

ADC+EDF=180 (LINEAR PAIR)

EDF=72

AED = FED (VOA)

SINCE

EFD is a triangle

EFD + EDF + FED =180 (ASM)

HENCE,

72+2 EFD=180

EFD=54

ALSO BFD is a triangle,

70+54+bcd=180