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]

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Solution

Calculation of angle: 1 Mark
Type of triangle: 1 Mark

In scalene triangles, all the angles are different. For $∠ A B C$ 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 $1^{\circ}$ and $2^{\circ}$ as the angles have an integral value. Hence, for a scalene triangle the maximum integral value of $∠ A B C = 177^{\circ}$ [Angle sum property of a triangle].
The following triangle will be an Obtuse angled triangle , because one of the angle is greater than $90 °$

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