Question

Given the regular polygon, find the measure of each numbered angle.

Answer 1

we know that 3 sided shape angles add up to 180
4 sides is 360
5 sided is 540
and 6 sided is 720

we have a 6 sided shape, all angles add up to 720
all sides of the shape are same length so the interior angles of the hexagon are 120
since we made triangles with sides going corner to corner I would just divide the interior angle by 2

Answer 2

if this method does not convince you then

Answer 3

get a compass and set it to any width, let's say 4cm
draw a circle, this means the circle has a radius 4cm
now draw a hexagon inside of the circle

you should find that the side lengths are equal to the radius, and that if you draw a line from the corner of a hexagon to the centre of the hexagon, you will notice that the corners meet the edge of the circle so the line from the corner of the hexagon to the centre is actually equal to the radius, 4cm

so you now have 6 points at the middle of the hexagon
you know the angles should add up to 360 in a circle

since we have 6 triangles in the hexagon, the centre has 6 angles in the centre
these should add up to 360

since all lines are equal length, we have triangles with equal angles at this point therefore 360/6 is 60 degrees

and as mentioned all sides are equal length, therefore all angles in the triangle are 60 degrees

so 1 and 2 are 60 degrees and 60 degrees

Answer 4

basically all triangles are equilateral and have same side lengths and same angle size
since all angles add to 180
180/3=60