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Question
The vertical angle of an isosceles triangle is three times the sum of its base angles. Find each angle.
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Solution
Let each base angle of an isosceles, triangle = x
Then its vertical = 3 (x + x)
= 3 × 2x
= 6x
∴ 6x + x + x = 180° ...(Sum of angles of a triangle)
⇒ 8x = 180°
⇒ x = `(180°)/8`
⇒ x = 22.5°
∴ Each base angle = 22.5°
and vertical angle = 3 × (22.5 + 22.5)
= 3 × 45
= 135°
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