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Question
Can a triangle have all angles less than 60°? Give reason for your answer.
Solution
We know, the sum of three angles of a triangle is equal to 180°.
If all the angles of a triangle are less than 60°, then each of the angle would be at least 59°.
⇒ Sum of the angles = 59° + 59° + 59°
⇒ Sum of the angles = 177°
⇒ The sum of the three angles of the triangle is not equal to 180°.
Similarly, for any value of the angles less than 59°, the sum of the three angles won’t be equal to 180°.
Thus, it won’t be a triangle.
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