Question

Given that AB || CD, intersected by a transversal, if the complement of ∠5 equals the supplement of ∠4, then the measures of ∠4 and ∠5 are

• A. ∠4 = 135^o, ∠5 = 45^o
• B. ∠4 = 45^o, ∠5 = 145^o
• C. ∠4 = 120^o, ∠5 = 80^o
• D. ∠4 = 105^o, ∠5 = 60^o

Answer 1

The correct option is A

∠4 = 135^o, ∠5 = 45^o

90^o - ∠5 = 180^o - ∠4,

And ∠4 + ∠5 = 180^o (Consecutive angles on same side of transversal)

Substituting the value of ∠4 in the first equation we get

∠5 = 45^o

Then �∠|4 = 135^o