Question

prove that if the arms of an angle are respectively parallel to the arms of another angle then the angles either have equal measure or they
supplementary

Answer 1

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.

If there is any confusion please leave a comment below.

Answer 2

Step-by-step explanation:

If the arms of one angle are respectively parallel to the arms of another angle, show that the two angles are either equal or supplementary. Solution : GIVEN Two angles ∠ABC and ∠DEF such that BA∣∣ED and BC∣∣EF. TO PROVE ∠ABC=∠DEFor∠ABC+∠DEF=180∘.