Question

ABCDEF IS A REGULAR HEXAGON . FIND EACH ANGLE OF TRIANGLE ABE

Answer 1

Interior Angles of a Regular Hexagon = 120°
Angle ABC = Angle DEF = 120°
Angle ABE = Angle BEF = 60°

In Triangle AEF,
Angle EFA = 120°
Angle AEF = Angle FAE
Angle AEF + Angle EFA + Angle FAE = 180°
Angle AEF + 120° + Angle FAE = 180°
Angle AEF + Angle FAE = 60°
Angle AEF = Angle FAE = 60°/2 = 30°

Angle BEF = Angle BEA + Angle AEF
60° = Angle BEA + 30°
Angle BEA = 30°

In Triangle ABE,
Angle ABE = 60°
Angle BEA = 30°
Angle ABE + Angle BEA + Angle EAB = 180°
60° + 30° + Angle EAB = 180°
Angle EAB = 90°

Answer 2

Sum of interior angle of regular hexagon = (2n -4)/n×90°

n=sides =6 sides = (2×6-4)/6 ×90°=

(12-4)/6 ×90° = 120°

Each angle=120°

Now we will take isosceles triangle that is triangle AFE

Angle EAF and angle AEF are equal

AFE is isosceles triangle and angle AFE =120°

120°+ x +x = 180°

2x + 120° = 180°

2x = 180- 120 = 60°

x = 30°

Now find angle EAB 120° -30° =90°

BE is a bisector so angle ABE =60°

90°+60° +x= 180°

x = 30°