Question

if the arms of the given angle is parallel to the arms of the other angle , show that the angles are either equal or supplementary

Answer 1

Two lines that form a right angle are perpendicular.By definition a right angle is 90 degrees.Since they are both 90 degrees they are equal.Two adjacent 90 degree angles form an 180 degree straight angle.Two angles that add to 180 degrees are supplementary.Therefore the angles are equal and supplementary.

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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