The sum of the measures of three angles of a triangle is greater than 180°. State whether the statement is true or false.

Solution:

Given, the sum of the measures of three angles of a triangle is greater than 180°.

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

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

A triangle is a closed figure formed by three line segments, consisting of interior as well as exterior angles.

The angle sum property formula for any polygon is expressed as, S = (n − 2) × 180°

where 'n' represents the number of sides in the polygon.

Number of sides of a triangle = 3

So, S = (3 - 2) × 180°

= 1 × 180°

S = 180°

Therefore, the sum of the interior angles of a triangle is always 180°.

✦ Try This: The sum of the measures of three angles of a triangle is less than 180°. 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 75

The sum of the measures of three angles of a triangle is greater than 180°. State whether the statement is true or false.

Summary:

The given statement,”The sum of the measures of three angles of a triangle is greater than 180°” is false.

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