Question

Each of the two equal angles of an isosceles triangle is four times the third angle. Find the angles of the triangle.

Answer 1

Let the third angle be x.

Then, the other two angles are 4x and 4x, respectively.

We know that, the sum of all three angles in a triangle is 180°.

i.e., ∠A + ∠B + ∠C = 180°

⇒ x + 4x + 4x = 180°

⇒ 9x = 180°

⇒ x = `180^circ/9` = 20°

Hence, the three angles are 4x = 4 × 20° = 80°, 4x = 4 × 20° = 80° and x = 20°.