It is possible to have a triangle in which each angle is less than 60°. State whether the statement is true or false.

Solution:

Given, it is possible to have a triangle in which each angle is less than 60°.

We have to determine if the given statement is true or false.

Consider the angles of a triangle less than 60 degrees.

Consider a triangle ABC,

Let ∠A = 50°, ∠B = 30° and ∠C = 40°

Sum of the angles = ∠A + ∠B + ∠C

= 50° + 30° + 40°

= 50° + 70°

= 120°

According to the angle sum property of a triangle, the sum of all three interior angles of a triangle is 180 degrees.

We observe that 120 degrees is less than 180 degrees.

The sum of interior angles of a triangle cannot be less than 180 degrees.

Therefore, a triangle cannot have each angle less than 60 degrees.

✦ Try This: It is possible to have a triangle in which each angle is less than 80°. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 81

It is possible to have a triangle in which each angle is less than 60°. State whether the statement is true or false.

Summary:

The given statement,”It is possible to have a triangle in which each angle is less than 60°” is false.

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