Question

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

Answer 1

In fig.,

x = a + b

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

Similarly a = c

But a + c + 30° = 180°

⇒ a + a + 30° = 180°

⇒ 2a + 30° = 180°

⇒ 2a = 180° − 30° = 150°

⇒ a =`(150°)/2=75°` and b + y = 90°

⇒ y + y = 90°

⇒ 2y = 90°

⇒ y =`(90°)/2=45°` ⇒ b = 45°

Hence x = a + b = 75° + 45° = 120° and y = 45°