In figure, ∆ABC is an equilateral triangle. Find the values of ∠x,

1.	In figure, ∆ABC is an equilateral triangle. Find the values of ∠x, ∠y and ∠z from the given figure.
Answer» ∵ ∆ABC is an equilateral triangle ∴AB = BC = CA ⇒ ∠ABC = ∠ACB = ∠BAC = 60° 60° = x + 22° (exterior angle property) x = 38° Also 38° + 22° + ∠z = 180° (by angle sum property of a ∆) ⇒ ∠z = 180° – 60° = 120° Again by exterior angle property ⇒ ∠ACB = ∠y + 38° ⇒ 60° = ∠y + 38° ⇒ ∠y = 22° Hence, ∠x = 38°, ∠y = 22° and ∠z = 120°

In figure, ∆ABC is an equilateral triangle. Find the values of ∠x, ∠y and ∠z from the given figure.

Answer»

∵ ∆ABC is an equilateral triangle

∴AB = BC = CA

⇒ ∠ABC = ∠ACB = ∠BAC = 60°

60° = x + 22°

(exterior angle property)

x = 38°

Also

38° + 22° + ∠z = 180°

(by angle sum property of a ∆)

⇒ ∠z = 180° – 60° = 120°

Again by exterior angle property

⇒ ∠ACB = ∠y + 38°

⇒ 60° = ∠y + 38°

⇒ ∠y = 22°

Hence, ∠x = 38°, ∠y = 22° and ∠z = 120°