Question

Apply the properties of isosceles and equilateral triangles to find the unknown angles in the given figure:

Answer 1

In the fig.,

a = b ..........(Angles opposite to equal sides)

∴ y = 120°

But a + 120° = 180° ..............(Linear pair)

⇒ a = 180°− 120° = 60°

∴ b = 60°

But x + a + b = 180° ...............(Angles of a triangle)

⇒ x + 60° + 60° = 180°

⇒ x + 120° = 180°

∴ x = 180°− 120° = 60°

b = z + 25 .........(Exterior angle of a triangle is equal to the sum of its interior opposite angles)

⇒ 60° = z + 25°

⇒ z = 60°− 25° = 35°

Hence x = 60°, y = 120° and z = 35°