In the figure, l || m and a transversal t cuts them. If ∠1: ∠2 = 2

1.	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» 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

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»

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