Answer :

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


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