Question
If there is a scalene ∆ABC in which all its angles have integral values, what would be the maximum possible value for ∠ABC? Which type of triangle would ∆ABC be, on the basis of its angles? [2 MARKS]
Answer:
:
Calculation of angle: 1 Mark
Type of triangle: 1 Mark
In scalene triangles, all the angles are different. For ∠ABC to be maximum, the other two angles must be minimum, but different (since scalene triangle).
The minimum value of the other angles will, therefore, be 1∘ and 2∘ as the angles have an integral value. Hence, for a scalene triangle the maximum integral value of∠ABC=177∘ [Angle sum property of a triangle].
The following triangle will be an Obtuse angled triangle , because one of the angle is greater than90°
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:
Calculation of angle: 1 Mark
Type of triangle: 1 Mark
In scalene triangles, all the angles are different. For ∠ABC to be maximum, the other two angles must be minimum, but different (since scalene triangle).
The minimum value of the other angles will, therefore, be 1∘ and 2∘ as the angles have an integral value. Hence, for a scalene triangle the maximum integral value of∠ABC=177∘ [Angle sum property of a triangle].
The following triangle will be an Obtuse angled triangle , because one of the angle is greater than90°
Was this answer helpful ?
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