find the sum of all interior angle of the following regular hexagon, octagon, decagon, polygon of all sides
Answers
Answer:
We will learn how to find the sum of the interior angles of a polygon having n sides.
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.
Triangle
Figure Triangle
3
(2n - 4) right angles
= (2 × 3 - 4) × 90°
= (6 - 4) × 90°
= 2 × 90°
= 180°
Quadrilateral
Figure Quadrilateral
4
(2n - 4) right angles
= (2 × 4 - 4) × 90°
= (8 - 4) × 90°
= 4 × 90°
= 360°
Pentagon
Figure Pentagon
5
(2n - 4) right angles
= (2 × 5 - 4) × 90°
= (10 - 4) × 90°
= 6 × 90°
= 540°
Hexagon
Figure Hexagon
6
(2n - 4) right angles
= (2 × 6 - 4) × 90°
= (12 - 4) × 90°
= 8 × 90°
= 720°
Heptagon
Figure Heptagon
7
(2n - 4) right angles
= (2 × 7 - 4) × 90°
= (14 - 4) × 90°
= 10 × 90°
= 900°
Octagon
Figure Octagon
8
(2n - 4) right angles
= (2 × 8 - 4) × 90°
= (16 - 4) × 90°
= 12 × 90°
= 1080°
Answer:
Step-by-step explanation: