Question

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

Answer 1

It is given that ∠7 = 80^o

From the figure we know that ∠7 and ∠8 form a linear pair of angles

So it can be written as

∠7 + ∠8 = 180^o

By substituting the values

80^o + ∠8 = 180^o

On further calculation

∠8 = 180^o – 80^o

By subtraction

∠8 = 100^o

From the figure we know that ∠7 and ∠5 are vertically opposite angles

So we get

∠7 = ∠5 = 80^o

From the figure we know that ∠6 and ∠8 are vertically opposite angles

So we get

∠6 = ∠8 = 100^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 = 80^o

∠2 = ∠6 = 100^o

∠3 = ∠7 = 80^o

∠4 = ∠8 = 100^o