Mathematics
Grade9
Easy

Question

A triangle’s angle measures are in the extended ratio of 1: 3: 6. Find the measures of the angles

  1. 18°, 54°, 108°
  2. 20°, 90°, 120°
  3. 36°, 27°, 162°
  4. 36°, 54°, 162°

hintHint:

The angle sum property of a triangle says that the sum of its interior angles is equal to 180°. Whether a triangle is an acute, obtuse, or a right triangle, the sum of the angles will always be 180°. This can be represented as follows: In a triangle ABC, ∠A + ∠B + ∠C = 180°.

The correct answer is: 20°, 90°, 120°


    A triangle’s angle measures are in the extended ratio of 1: 3: 6.
    Let the angles of a triangle be 1x, 3x and 6x

    By angle sum property :
    The angle sum property of a triangle says that the sum of its interior angles is equal to 180°. Whether a triangle is an acute, obtuse, or a right triangle, the sum of the angles will always be 180°. This can be represented as follows: In a triangle ABC, ∠A + ∠B + ∠C = 180°.
    1x +3x+ 6x = 180°
    10x = 180°
    x = 18°
    The angles = 1x = 1 cross times 18°=  18°
    3x = 3 cross times 18° = 54°
    6x = 6 cross times 18° = 108°
    Thus, the measures of the angles are 18°,  54° and 108°

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