In the figure given below $$L_1 \mid \mid L_2$$ then x = ______________.

Let $$\angle\ HBG$$ = 2y

$$\angle\ BAF$$ = 2y (corresponding angles are equal)

$$\angle\ FAC\ =\ \angle\ CAB$$ = y

$$\angle\ ABG$$ = 180 - 2y

$$\angle\ ABC\ =\ \angle\ CBG$$ = 90 - y

Sum of all angles of a triangle = $$180^{\circ\ }$$

In traingle, $$\angle\ CAB$$ = y, $$\angle\ ABC$$ = 90-y

y + 90 - y + $$\angle\ ACB$$ = 180

$$\angle\ ACB$$ = $$90^{\circ\ }$$

$$\angle\ ECB$$ = 180 - 90 = 90

2x = 90

x = $$45^{\circ\ }$$

Answer is option B