Question
Is it possible to have a triangle, in which.
Each angle is greater than 60°?
Each angle is greater than 60°?
✓
Answer
Give reasons in support of your answer in. No, because if each angle is greater than 60°, then the sum of all three angles will be greater than 180°, which is not possible.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 of the given triangle are greater than 180°, which is not possible for a triangle. Hence, we can say that it is not possible for each angle of a triangle to be greater than 60°
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 of the given triangle are greater than 180°, which is not possible for a triangle. Hence, we can say that it is not possible for each angle of a triangle to be greater than 60°
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