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
• B. Right-angled and isosceles
• C. Acute-angled and isosceles
• D. Acute-angled and scalene

Answer 1

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.