Question

The ratio of the same side angles of two parallel lines is 1:14. Find all angles.

Answer 1

Answer:

∠1=∠3=∠5=∠7=168°

∠6=∠4=∠2=∠8=12°

Step-by-step explanation:

We are given two angles of the same side of parallel lines is 1:14

Please see the attachment to see all angles of parallel lines.

In figure, ∠6 and ∠3 are same side angles.

∠6 : ∠3 = 1 : 14

Therefore, ∠6 = x ,  ∠3=14x

Sum of angles of same side of parallel lines is 180°

∠6 + ∠3  = 180°

x+14x=180°

x=12

∠6=12°

∠3=168°

∠3=∠1=168°   (Vertically Opposite angles)

∠3=∠5=168°   (Alternate interior angles)

∠3=∠7=168°    (Corresponding angles)

Therefore, ∠1=∠3=∠5=∠7=168°

∠6=∠8=12°   (Vertically Opposite angles)

∠6=∠4=12°     (Alternate interior angles)

∠6=∠2=12°     (Corresponding angles)

Therefore, ∠6=∠4=∠2=∠8=12°