Question

In the given figure, ABCD is a parallelogram, AD = AE, BAE is a straight line, ∠ABC = 88°, ∠EAF = 162° and ∠AFC = 48°. Then ∠BCF equals.

(a) 18°

(b) 28°

(c) 22°

(d) 32°

Answer 1

Correct option is (c) 22°

In parallelogram ABCD,

∠B = 88°

then, ∠BCD = 180° − ∠B = 180° − 88° = 92° (Adjacent angles of a parallelogram)

Also, ∠B + ∠BAD = 180°

88° + ∠BAD = 180°

∠BAD = 92°

and, ∠B = ∠ADC = 88° (Opposite angles of parallelogram are equal)

Now, ∠FAB = 180° − ∠EAF = 180° − 162° = 18°

Now, In quadrilateral FADC,

∠F + ∠FAD + ∠ADC + ∠DCF = 360°

48° + (18° + 92°) + 88° + ∠DCF= 360°

∠DCF = 114°

Now, ∠BCF = ∠DCF − ∠BCD

∠BCF = 114° − 92° 

= 22°