Question

In the given figure, l ||m in and a transversal I cuts them. If $\angle 1:\angle 2=2:3$, find the measure of each of the marked angles.

Answer 1

Let ∠1 = 2 k and ∠2 = 3k , where k is some constant.

Now, ∠1 and ∠2 form a linear pair.

∴ ∠1 + ∠2 = 180

⇒ 2k + 3 k = 180

⇒ 5k = 180

⇒ k = 36

∴ ∠1 = 2k = 2 × 36 = 72

∠2 = 3k = 3 × 36 = 108

Now,

∠3 = ∠1 = 72 (Vertically opposite angles)

∠4 = ∠2 = 108 (Vertically opposite angles)

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

∴ ∠5 = ∠1 = 72 (Pair of corresponding angles)

∠6 = ∠2 = 108 (Pair of corresponding angles)

∠7 = ∠1 = 72 (Pair of alternate exterior angles)

∠8 = ∠2 = 108 (Pair of alternate exterior angles)