Question

the hexagon ABCDEF, AB is parallel to ED and AF is parallel to CD. Angle ABC = 90°, angle CDE = 140° and Angle DEF is 120 degrees. Calculate angle EFA

Answer 1

Given :  hexagon ABCDEF,

AB is parallel to ED

AF is parallel to CD.

Angle ABC = 90°, angle CDE = 140° and Angle DEF is 120 degrees.

To Find : angle EFA

Solution:

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent.  

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Interior angles are supplementary. ( adds up to 180°)

Draw a line EM || CD   and  AF

as CD || AF Given

=> ∠DEM + ∠CDE = 180°   Interior angles are supplementary

=> ∠DEM + 140° = 180°

=> ∠DEM = 40°

∠FEM + ∠DEM = ∠DEF

=> ∠FEM + 40° = 120°

=> ∠FEM =80°

∠FEM  +  ∠EFA = 180°   Interior angles are supplementary

=> 80°  +  ∠EFA = 180°

=> ∠EFA = 100°

∠EFA = 100°

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