Question

In the hexagon ABCDEF, BC is parallel to ED and DC is parallel to EF. Angle DEF = 109 degrees and angle EFA= 95 degrees.
Angle FAB is equal to angle ABC.
Find the size of an angle EDC and angle FAB.

Answer 1

Given :  In the hexagon ABCDEF, BC is parallel to ED and DC is parallel to EF. ∠DEF = 109° and ∠EFA= 95° . ∠FAB = ∠ ABC

To find :  ∠EDC & ∠FAB

Solution:

DC || EF

=> ∠DEF + ∠EDC = 180°

=> 109° + ∠EDC = 180°

=> ∠EDC = 71°

BC || ED

=> ∠EDC + ∠DCB = 180°

=> ∠DCB =  109°

Sum of all angles of  Hexagon = 720°

=>  95° + 109° + 71° + 109° + ∠FAB + ∠ ABC = 720°

∠FAB = ∠ ABC given

=> 384 + ∠FAB + ∠ FAB  = 720°

=>  2∠FAB   =  336°

=> ∠FAB   =  168°

∠EDC = 71°  , ∠FAB   =  168°  

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