Question

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

Answer 1

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

∴ ∠7 + ∠8 = 180${}^o$

⇒ 80${}^o$ + ∠8 = 180${}^o$

⇒ ∠8 = 180${}^o$ − 80${}^o$ = 100v

Now,

∠6 = ∠8 = 100${}^o$ (Vertically opposite angles)

∠5 = ∠7 = 80${}^o$ (Vertically opposite angles)

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

∴ ∠1 = ∠5 = 80${}^o$

(Pair of corresponding angles)

∠2 = ∠6 = 100${}^o$ (Pair of corresponding angles)

∠3 = ∠7 = 80${}^o$ (Pair of corresponding angles)

∠4 = ∠8 = 100${}^o$ (Pair of corresponding angles)