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The sum of interior angles of a polygon of n sides is __________right angles. Fill in the blanks to make the statement true.

Solution:

Given, The sum of interior angles of a polygon of n sides is __________right angles.

We have to fill in the blanks to make the statement true.

The angles that lie inside a shape, are said to be interior angles, or the angles that lie in the area bounded between two parallel lines that are intersected by a transversal are also called interior angles.

We know that the sum of all the interior angles of a polygon is (n - 2) x 180°,

where n is the number of sides of the polygon.

Right angle means 90 degrees.

On rewriting(n - 2) × 180°, we get

(n - 2) x 180° = (n - 2) × 2(90°)

= 2(n - 2) × 90°

= [2(n) - 2(2)] × 90°

= (2n - 4) × 90°

Therefore, the required sum of interior angles of a polygon is (2n - 4) x 90°.

✦ Try This: The sum of interior angles of a polygon of n sides is __________ 45 degrees. Fill in the blanks to make the statement true.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 69

The sum of interior angles of a polygon of n sides is __________right angles. Fill in the blanks to make the statement true.

Summary:

The sum of interior angles of a polygon of n sides is (2n - 4) right angles.

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