Find the unknown angle from the following figure if p ॥ q.

1.	Find the unknown angle from the following figure if p ॥ q.
Answer» ∠e + 125° = 180°, (Linear pair angle) ⇒ ∠e = 180° – 125° = 55°, ∠e = ∠f = 55°, (Vertically opposite angles) In figure, p ॥ q and t is a transversal ∠a = ∠f, (Alternate angle) ∠a = 55°, (∵ ∠f = 55°) ∠d = 125°, (Corresponding angels) ∠c = ∠a = 55°, (Vertically opposite angles) and ∠b = ∠d = 125°, (Vertically opposite angles) Thus, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠d = 125°, ∠e = 55° and ∠f= 55°

Answer»

∠e + 125° = 180°, (Linear pair angle)

⇒ ∠e = 180° – 125° = 55°,

∠e = ∠f = 55°, (Vertically opposite angles)

In figure, p ॥ q and t is a transversal

∠a = ∠f, (Alternate angle)

∠a = 55°, (∵ ∠f = 55°)

∠d = 125°, (Corresponding angels)

∠c = ∠a = 55°, (Vertically opposite angles)

and ∠b = ∠d = 125°, (Vertically opposite angles)

Thus, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠d = 125°, ∠e = 55° and ∠f= 55°

Discussion