Make the following number sequences from the sequence of equilateral triangle, square, regular Pentagon and so on of regular polygons Number of side =3,4,5...
Sum of interior angles
Sum of exterior angles 1 interior angles 1 exterior angles
Answers
Given:
The sequence of an equilateral triangle, square, regular pentagon and so on of regular polygons Number of side = 3, 4, 5 ...
To find:
Sum of interior angles
Sum of exterior angles
1 interior angle
1 exterior angle
Solution:
Sum of interior angles
Sum of interior angles of a regular polygon of n sides
= n × [ (n - 2)180° ]/2
= (n - 2)180°
∴ Sum of interior angles of equilateral triangle (n = 3), square (n = 4), regular pentagon (n = 5), etc are:
180°, 360°, 540°, ..........
Sum of exterior angles
Sum of exterior angles of a regular polygon of n sides
= n × 180° - (n - 2) × 180°
= 2 × 180°
= 360°
which is free from "n".
1 interior angle
One interior angle of triangle, square, regular pentagon etc are,
180°/3, 360°/4, 540°/5,.......
= 60°, 90°, 180°,.........
1 exterior angle
One exterior angle of triangle, square, regular pentagon etc are,
360°/3, 360°/4, 360°/5,.......
= 120°, 90°, 72°,.........
The sequence of sum of inner angles is
180,360,540,720,
The sequence of sum of outer angle is
360,360,360,
The sequence of one inner angle is 60,90,108,120