Maharashtra BoardEnglish MediumSTD 7MathsProperties of Triangles3 Marks
Question
Is it possible to have a triangle, in which.
Each angle is equal to 60°
✓
Answer
Give reasons in support of your answer in. Yes, if each angle of the triangle is equal to 60°, then the sum of all three angles will be 180° , which is 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 of the given triangle is equal to 180°, which is possible in case of a triangle. Hence, we can say that it is possible for each angle of a triangle to be equal to 60°
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