Question

Can a triangle have all angles less than ${60}^0$? Give reason for your answer.

Answer 1

According to the angle sum property, the sum of interior angles of a triangle is ${180}^0$

Now, considering angles less than ${60}^0$,

Let us take ${59}^0$, which is the highest natural number less than ${60}^0$.

Then we obtain

${59}^0+{59}^0+{59}^0={177}^0\ne {180}^0$

we can say that if all the angles are less than ${60}^0$, the measure of the angles won’t satisfy the angle sum property of a triangle.

Hence, a triangle cannot have all angles less than ${60}^0$.