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 = ${\displaystyle \frac{180°}{8}=22.5°}$

∴ Each base angle = 22.5°
and vertical angle = 3 × (22.5 + 22.5)
= 3 × 45 = 135°