Question

If ABC= 6, DEF= 120 and ABE =10 then find the value of ABCD.​

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°

hope it helps you...