Question

In the given figure, l || m and a transversal t cuts them. If ∠7 = 80°, find the measure of each of the remaining marked angles.

Answer 1

In the given figure, ∠7 and ∠8 form a linear pair.

∴ ∠7 + ∠8 = 180º

⇒ 80º + ∠8 = 180º

⇒ ∠8 = 180º − 80º = 100º

Now,

∠6 = ∠8 = 100º (Vertically opposite angles)

∠5 = ∠7 = 80º (Vertically opposite angles)

It is given that, l || m and t is a transversal.

∴ ∠1 = ∠5 = 80º (Pair of corresponding angles)

∠2 = ∠6 = 100º (Pair of corresponding angles)

∠3 = ∠7 = 80º (Pair of corresponding angles)

∠4 = ∠8 = 100º (Pair of corresponding angles)