In the given figure, AB || CD and EF is a transversal. If ∠8 = 110°, find each one of the unknown angles, marked in the figure. Give reasons.

Given:

AB || CD

EF is a transversal

∠8 = 110°

Let's find angles at the bottom intersection (Point on CD):

∠5 = ∠8 $\quad$[Vertically opposite angles]

∴ ∠5 = 110°

Since CD is a straight line, the angles ∠7 and ∠8 form a linear pair and must sum to 180°.

∴ ∠7 + ∠8 = 180°

⇒ ∠7 + 110° = 180° $\quad$[Substituting the value of ∠8]

⇒ ∠7 = 180° - 110°

⇒ ∠7 = 70°

∠6 = ∠7 $\quad$[Vertically opposite angles]

∴ ∠6 = 70°

Let's find angles at the top intersection (Point on AB):

∠4 = ∠8 $\quad$[Corresponding angles]

∴ ∠4 = 110°

∠1 = ∠4 $\quad$[Vertically opposite angles]

∴ ∠1 = 110°

Since AB is a straight line, the angles ∠1 and ∠2 form a linear pair and must sum to 180°.

∴ ∠1 + ∠2 = 180°

⇒ 110° + ∠2 = 180° $\quad$[Substituting the value of ∠1]

⇒ ∠2 = 180° - 110°

⇒ ∠2 = 70°

∠3 = ∠2 $\quad$[Vertically opposite angles]

∴ ∠3 = 70°

∠5 = 110°, ∠6 = 70°, ∠7 = 70°, ∠1 = 110°, ∠2 = 70°, ∠3 = 70°, ∠4 = 110°