GEOMETRY: Interior, Exterior angles of any polygon, ratio of the angles

Interior angles of any polygon

Ia = 180(s - 2)


where:

Ia = sum of all interior angles of any polygon

s = number of sides of the polygon


for triangles: Ia = 180

for rectangles, trapezoids, quadrilaterals, parallelograms and any four-sided polygons: Ia = 360

for a pentagon: Ia = 540

for a hexagon (hex-bolt): Ia = 720


Exterior angles of any polygon

Ea = 360


where:

Ea = sum of all exterior angles of any polygon


1. Determine the largest angle of a Triangle if the ratio of the angles is 1:3:5

find:

x = shortest angle

5x = largest angle of triangle

solution:

1x + 3x + 5x = 180

9x = 180

x = 180/9

x = 20

3x = 3 * 20 = 60

5x = 5 * 20 = 100