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Question

If the measures of the angles of a triangle are in the ratio 1:2:3, then how can the triangle be classified?

A

Right-angled and scalene

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B

Right-angled and isosceles

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C

Acute-angled and isosceles

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D

Acute-angled and scalene

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Solution

The correct option is A Right-angled and scalene Since the ratio of the angles is given as 1:2:3, let the angles measure x, 2x, and 3x. According to the angle sum property of a triangle, the sum of the measures of the angles of a triangle is 180°. Therefore x+ 2x + 3x= 180° ⇒ 6x= 180° ⇒ x= 30° Thus, the angles of the triangle measure 30°, 2 × 30° = 60°, and 3 × 30° = 90°. Since all angles of the triangle are of different measures, the triangle is scalene. Also, since one of the angle measures 90°, the triangle is right-angled. Thus, the triangle is right-angled and scalene.

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