Question

prove that the sum of all internal angles of a polygon is (2n - 4) right angles

Answer 1

We know that if a polygon has ‘n’ sides, then it is divided into (n – 2) triangles. 

We also know that, the sum of the angles of a triangle = 180°.

Therefore, the sum of the angles of (n – 2) triangles = 180 × (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.

Thus, each interior angle of the polygon = (2n – 4)/n right angles.