Question

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

Answer 1

In fig.,

a = 70°  ...........(Angles opposite to equal sides)

But a + 70° + x = 180° ...........(Angles of a triangle)

⇒ 70° + 70° + x = 180°

⇒ 140° + x = 180°

⇒ x = 180° − 140° = 40°

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

But a = y + b ...........(Exterior angle of a triangle is equal to sum of its interior opposite angles)

⇒ 70° = y + y 

⇒ 2y = 70°

⇒ y =`(70°)/2=35°`

Hence x = 40°, y = 35°