Question

The vertical angle of an isosceles triangle is three times the sum of its base angles. Find each angle.

Answer 1

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°