Question

Given ABC,DB,AC and <1=<2 prove <3=<4

Answer 1

From the figure

angle 1 = angle 2

Angle 1 is alternate to angle 3

Alternate angles are equal

Therefore, angle 1 = angle 3

Angle 2 is alternate to angle 4

Alternate angles are equal

Therefore, angle 2 = angle 4

Angle 1 = Angle 3

Angle 2 = Angle 4

Since Angle 1 = Angle 2

Hence, Angle 3 = Angle 4