Question

Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in figure and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.

Answer 1

∠1 = 120°   ......(i) [Vertically opposite angles]

c || f and a is transversal.

∴ ∠1 + ∠x = 180°  ......[Co-interior angles]

⇒ 120° + ∠x – 180°   ......[Using (1)]

⇒ ∠x = 180° – 120° = 60°

Now, a || d and c is a transversal.

⇒ ∠x + ∠2 = 180°   ......[Co-interior angles]

⇒ 60° + ∠2 = 180°   ......[Using (ii)]

⇒ ∠2 = 180° – 60° = 120°

⇒ ∠2 = ∠y = 120°  ......[Vertically opposite angles]

Also, a || d and f is a transversal.

∴ ∠1 + ∠z = 180°  ......[Co-interior angles]

⇒ 120° + ∠z = 180°  ......[Using (i)]

⇒ ∠z = 180° – 120° = 60°

Thus, ∠x = 60°, ∠y = 120° and ∠z = 60°