Question

for the sequences of regular polygons starting with an equilateral triangle ,write the algebraic expression for the sequences of the sum if interior angels , and the sum of the exterior angls5 , the measures if an interior angels and the measures of an exterior angles

Answer 1

If n is the number of sides


The sum if interior angels:

(n - 20) 180


The sum of exterior angles

= 360/n  x n = 360



Measure of interior angle

180 - 360/n



Measure of exterior angles

360/n

Answer 2

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°,.........