Step-by-step explanation:
as a regular polygon (in our case 6 corners and sides) all sides are equally long, and all angles are also of equal size. so, the graphic is optically misleading.
so,
a) the congruent triangles are ABC, CDE and EFA.
b)i)
any internal angle of a regular polygon with n corners/angles is (n-2)×180/n.
our n here is 6.
angle ABC = (6-2)×180/6 = 4×30 = 120 degrees.
ii)
the sum of all angles in a triangle is 180 degrees.
the triangle ABC is an isoceles triangle (the legs are equally long), and so, both "side angles" are equal. and we know the angle ABC.
so,
180 = 120 + 2×side-angle
60 = 2×side-angle
side-angle = CAB = 60/2 = 30 degrees.
iii)
as we know that all inner angles of the regular polygon are equally sized, angle FAB = angle ABC = 120 degrees.
and angle FAE = angle CAB = 30 degrees.
so,
angle EAC = 120 - angle CAB - angle FAE =
= 120 - 30 - 30 = 60 degrees
c) equilateral triangle
