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
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Answers
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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