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