Mathematics
Grade9
Easy
Question
A triangle’s angle measures are in the extended ratio of 1: 3: 6. Find the measures of the angles
- 18°, 54°, 108°
- 20°, 90°, 120°
- 36°, 27°, 162°
- 36°, 54°, 162°
Hint:
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 18°= 18°
3x = 3 18° = 54°
6x = 6 18° = 108°
Thus, the measures of the angles are 18°, 54° and 108°
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