Question

Show that the sum of the measures of the external angles of any polygon is 360°. [ HINT:- Draw three different polygons like a triangle, quadrilateral, pentagon. Extend each side, then measure the exterior angles from there. Finally, find the sum of measures of all exterior angles of each polygon.]

Answer 1

basically get a shape

eg we will work with triangles,, add angles to the inside,, ensuring they add up to 180 (because angles in a triangle add up to 180)

now that we have the angles,, extend each side with a line to show the exterior angles.

we know that angles on a line add up to 180,, so to find the external angle,, we can use our internal angle

you would use:

[ 180- internal angle]

do this for all external angles

add all your answers together,, should equal to 180