Question

In the figure, l || m and a transversal t cuts them. If ∠1: ∠2 = 2: 3, find the measure of each of the marked angles.

Answer 1

It is given that ∠1: ∠2 = 2: 3

From the figure we know that ∠1 and ∠2 form a linear pair of angles

So it can be written as

∠1 + ∠2 = 180^o

By substituting the values

2x + 3x = 180^o

On further calculation

5x = 180^o

By division

x = 180^o/5

x = 36^o

By substituting the value of x we get

∠1 = 2x = 2 (36^o) = 72^o

∠2 = 3x = 3 (36^o) = 108^o

From the figure we know that ∠1 and ∠3 are vertically opposite angles

So we get

∠1 = ∠3 = 72^o

From the figure we know that ∠2 and ∠4 are vertically opposite angles

So we get

∠2 = ∠4 = 108^o

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

So the corresponding angles according to the figure is written as

∠1 = ∠5 = 72^o

∠2 = ∠6 = 108^o

∠3 = ∠7 = 72^o

∠4 = ∠8 = 108^o

Comments

Good best

---

But there is one more easy way