Question

A B C D E F IS A REGULAR HEXAGON.FIND EACH ANGLE OF TRIANGLE ABE ??

Answer 1

Solution:-
Given that ABCDEF is a regular hexagon, so all sides of it are equal in length.
Sum of the angles of a (n - 2)180
n = number of sides.
Sum of the angles of hexagon is 720°, since it is a regular hexagon and each interior angle has measure 120°.
Quadrilateral ABEF contains half the angle measure of hexagon; its interior angle measure 360°.
Δ AFE = 120° 
Δ AFE is isosceles ; ∠ FAE = ∠ FEA = 30°
Sum of the angles of triangle = 180°
∠ FAE + ∠ EAB = 120°; therefore ∠ EAB = 90°
∠ ABE is one half of the 120° = 60°
∠ ABE + ∠ EAB + ∠ AEB = 180°
⇒ 60° + 90° + 30° = 180°
⇒ ∠ ABE = 60°; ∠ EAB = 90° and ∠ AEB = 30°  Answer.

Answer 2

Answer:

All sides of hexagon are equal in length

Sum of angles of a polygon = (n - 2)180

n = number of sides

Sum of angles of a hexagon is 720°, since it is a regular

hexagon each interior angle has measure 120°

Quadrilateral ABEF contains half the angle measure of the

hexagon; its interior angle measure = 360°

angle AFE = 120° (angle of hexagon ABCDEF)

triangle AFE is isosceles; angle FAE = angle FEA = 30°

sum of angles of triangle = 180°

angle FAE + angle EAB = 120°; therefor angle EAB = 90°

angle ABE is one half of 120° = 60°

angle ABE + angle EAB + angle AEB = 180°

therfor angle AEB = 30°