Question

13. In the following figure, AC || BD, LCAF
= 25°, LDBG = 65° and BF=BA. Then,
LBFE is equal to
25°
16 in
65°
A
B
G
a) 90°
c) 140°
b) 1550
d) 1650​

Answer 1

given ,. ∠CAE = 25° & ∠GBD =65°

since , AC II BD

∠BAC = ∠GBD ( corresponding angles )

∠BAC = ∠GBD = 65°

∠BAC = ∠CAE + ∠BAE = 65°

∠BAC = 25° + ∠BAE = 65°

∠BAE = ∠BAF = 65° - 25°

∠BAF = 40°

it's also given that, BF = BA

then , ∠BAF = ∠AFB = 40°

( angles opposite to equal sides are equal )

∠BFE + ∠AFB = 180° ( angles on straight line )

∠BFE = 180° - ∠AFB

∠BFE = 180° - 40°

∠BFE = 140°. ( option C )