Question

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

Answer 1

Step-by-step explanation:

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 = 22.5°

∴ Each base angle = 22.5°

And vertical angle = 3 × (22.5 + 22.5)

= 3 × 45 = 135°

Answer 2

Answer:

base angles 22.5 and top angle 135.......

Step-by-step explanation:

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 = 22.5°

∴ Each base angle = 22.5°

And vertical angle = 3 × (22.5 + 22.5)

= 3 × 45 = 135°