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

1.	In the given figure, l \|\| m and a transversal t cuts them. If ∠1 = 120°, find the measure of each of the remaining marked angles.
Answer» It is given that ∠1 = 120^o 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 120^o + ∠2 = 180^o On further calculation ∠2 = 180^o – 120^o By subtraction ∠2 = 60^o From the figure we know that ∠1 and ∠3 are vertically opposite angles So we get ∠1 = ∠3 = 120^o From the figure we know that ∠2 and ∠4 are vertically opposite angles So we get ∠2 = ∠4 = 60^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 = 120^o ∠2 = ∠6 = 60^o ∠3 = ∠7 = 120^o ∠4 = ∠8 = 60^o

In the given figure, l || m and a transversal t cuts them. If ∠1 = 120°, find the measure of each of the remaining marked angles.

Answer»

It is given that ∠1 = 120^o

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

120^o + ∠2 = 180^o

On further calculation

∠2 = 180^o – 120^o

By subtraction

∠2 = 60^o

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

So we get

∠1 = ∠3 = 120^o

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

So we get

∠2 = ∠4 = 60^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 = 120^o

∠2 = ∠6 = 60^o

∠3 = ∠7 = 120^o

∠4 = ∠8 = 60^o