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