Question

If the arms of one of the angles are respectively parallel to the arms of another angle show that the two angles are either equal or supplementary

Answer 1

There is your answer

Answer 2

Thank you for asking this question:

here is your answer:

BA || ED and BC is a traversal,

∴ ∠EGB = ∠ABC (these are the alternate angles)

BC || EF and DE is a traversal,

∠DEF + ∠EGB = 180° (these are the co interior angles)

∠DEF + ∠ABC = 180° (∴∠EGB = ∠ABC)

Or ∠ABC and ∠DEF are supplementary.

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