Question

The figure below shows a straight line AB intersected by another straight line t:

Answer 1

Answer:

As ∠1 and ∠4 makes straight line t so their sum should be equal to 180°

∠1 + ∠4 = 180° (makes pair of supplementary angles)------------------------(1)

Similarly ∠3 and ∠4 makes straight line AB so their sum should also be equal to 180°

∠3 + ∠4 = 180° (makes pair of supplementary angles)------------------------(2)

From equations (1) and (2) we get

∠1 + ∠4 = ∠3 + ∠4 (as both were equal to 180°)

subtracting ∠4 from both sides we get

∠1 + ∠4 - ∠4 = ∠3 + ∠4 -∠4

∠1 = ∠3

Hence, proved that verticaly opposite angles ∠1 and ∠3 are equal