Suppose that a polygon has ‘n’ sides, then it is to be divided into (n - 2) triangles.
We know that, the sum of the interior angles of a triangle = 180°.
Therefore, the sum of the angles of (n - 2) triangles = 180 × (n - 2)
= 2 × 90 × (n - 2)
= 2 right angles × (n – 2)
= 2(n – 2) right angles
= (2n – 4) right angles
Therefore,
the sum of interior angles of a polygon having n sides is (2n – 4) right angles.
Hence,
the sum of the interior angles of a pentagon (n = 5)
= (2n - 4) right angles
= (2 × 5 - 4) × 90°
= (10 - 4) × 90°
= 6 × 90°
= 540°
