Make the following number sequences, from the sequence of equilateral triangles, squares, regular pentagons and so on, of regular polygons. Arithmetic sequence . 10 standard mathematics

1)Make the following number sequences, from the sequence of equilateral triangles, squares, regular pentagons and so on, of regular polygons:

 No. Of sides.                               3,4,5,.....

Sum of inner angles 

One inner angle

One outer angle


Ans:

     No.of sides :3,4,5

      Sum of inner angles:


Sum of inner 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 outer 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°,.........



  

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