Let’s write then measurement of each interior and exterior angle of the following regular polygon.

Pentagon

To find the sum of measurements of the interior angles of a polygon, we have formula which will make our computation very simpler and easy.

We know that if a polygon has n sides, then it can be easily divided into n – 2 triangles.

For example a quadrilateral can be divided into two triangles by a diagonal.

Sum of all angles in a triangle is 180°.

So sum of n – 2 angles will be = 180 × (n – 2)

= 2 right angles × (n – 2)

= (2n – 4) right angles

Measure of each angle in a polygon of n sides is given as = (2n – 4) / n

Now for a pentagon, we know it has five sides. So let us substitute n = 5 in the formula.

Sum of interior angles is given as = (2 × 5 – 4) × 90

= (10 – 4) × 90

= 6 × 90

= 540°

Measure of each interior angle in pentagon = Sum of all Interior Angles / n

= 540 / 5

= 108°

Sum of all exterior angles in a regular of n sides is always 360°.

Measure of each exterior angles for pentagon = 360 / 5
= 72° Tagging |||Maths||Geometrical Proofs||Geometrical Proofs

Difficulty ||| Medium