Question
Is it possible to have a triangle, in which. Each angle is less than $60^\circ $?
✓
Answer
Give reasons in support of your answer in.
No, because if each angle is less than $60^\circ$ , then the sum of all three angles will be less than $180^\circ$ ,
which is not possible in case of a triangle.
Proof:
Let the three angles of the triangle be $\angle \text{A},\angle \text{B}$ and $\angle \text{C}$ As per the given information,
$\angle \text{A}<60^\circ...(\text{i})$
$\angle \text{B}<60^\circ...(\text{ii})$
$\angle \text{C}<60^\circ...(\text{iii})$ On adding $(i), (ii)$ and $(iii)$,
we get: $\angle \text{A}+\angle \text{B}+\angle \text{C}<60^\circ+60^\circ+60^\circ$ $\angle \text{A}+\angle \text{B}+\angle \text{C}<180^\circ$ We can see that the sum of all three angles is less than $180^\circ$ , which is not possible for a triangle.
Hence, we can say that it is not possible for each angle of a triangle to be less than $60^\circ$
No, because if each angle is less than $60^\circ$ , then the sum of all three angles will be less than $180^\circ$ ,
which is not possible in case of a triangle.
Proof:
Let the three angles of the triangle be $\angle \text{A},\angle \text{B}$ and $\angle \text{C}$ As per the given information,
$\angle \text{A}<60^\circ...(\text{i})$
$\angle \text{B}<60^\circ...(\text{ii})$
$\angle \text{C}<60^\circ...(\text{iii})$ On adding $(i), (ii)$ and $(iii)$,
we get: $\angle \text{A}+\angle \text{B}+\angle \text{C}<60^\circ+60^\circ+60^\circ$ $\angle \text{A}+\angle \text{B}+\angle \text{C}<180^\circ$ We can see that the sum of all three angles is less than $180^\circ$ , which is not possible for a triangle.
Hence, we can say that it is not possible for each angle of a triangle to be less than $60^\circ$
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