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
Measure of each interior angle in pentagon = Sum of all Interior Angles / n
= 540 / 5
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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