In the given figure, l || m and a transversal t cuts them. If ∠7 = 80°,
Question:

In the given figure, $I \| m$ and a transversal $t$ cuts them. If $\angle 7=80^{\circ}$, find the measure of each of the remaining marked angles.

Solution:

In the given figure, ∠7 and ∠8 form a linear pair.

∴ ∠7 + ∠8 = 180º

⇒ 80º + ∠8 = 180º

⇒ ∠8 = 180º − 80º = 100º

Now, 

∠6 = ∠8 = 100º       (Vertically opposite angles)

∠5 = ∠7 = 80º         (Vertically opposite angles)

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

∴ ∠1 = ∠5 = 80º      (Pair of corresponding angles)

∠2 = ∠6 = 100º         (Pair of corresponding angles)

∠3 = ∠7 = 80º           (Pair of corresponding angles)

∠4 = ∠8 = 100º         (Pair of corresponding angles)

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