Question

In the given figure, l || m and a transversal t cut them. If $\angle 1={120}^{\circ }$, find the measure of each of the remaining marked angles.

Answer 1

We have, ∠1 = 120°. Then,

∠1 = ∠5 (Corresponding angles) ⇒ ∠5 = 120°

∠1 = ∠3 (Vertically-opposite angles ) ⇒ ∠3 = 120°

∠5 = ∠7 (Vertically-opposite angles) ⇒ ∠7 = 120°

∠1 + ∠2 = 180° (Since AFB is a straight line) ⇒ 120° + ∠2 = 180° ⇒ ∠2 = 60°

∠2 = ∠4 (Vertically-opposite angles) ⇒ ∠4 = 60°

∠2 = ∠6 (Corresponding angles) ⇒ ∠6 = 60°

∠6 = ∠8 (Vertically- opposite angles) ⇒ ∠8 = 60°

∴∠1 = 120°, ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°,∠6 = 60°, ∠7 = 120° and ∠8 = 60°