Question

Can a triangle have all angles less than 60°?
Give reason for your answer.

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Answer 1

✨Hi mate here is the answer:-✨

Question:

Can a triangle have all angles less than 60°? Give reason for your answer.

Solution:

We know that the sum of three angles of a triangle is 180°

According to the question

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.

✨Hope it helps you...✨

Answer 2

Question:-

Can a triangle have all angles less than 60°?

Give reason for your answer.

______________________________

$\huge\sf\underline{\underline{Answer:}}$

No, a triangle cannot have all angles less than 60° because if all the angles of triangle are less than 60° , then their sum will not reach upto 180°. If all the angles have angles less than 60°, then a triangle cannot be formed .

A triangle can be formed when it has its angles greater than 60° or equals to 60°

For example:-

$\angle$60°+60° = 120° +60° = 180°

$\angle$130°+20°=150°+30° = 180°

A triangle cannot be formed with angles less than 60°.

For example:-

$\angle$30°+40° = 70°+40° = 110°.

$\angle$40°+40° = 80°+50° = 130°.

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Hence,proved.