Proof: Its is given that ∠1 and ∠2 are supplementary. ∠1 and ∠3 are also supplementary, so _______Since ∠2 and ∠3 are corresponding angles, a║b.A. ∠3 and ∠2 are supplementary.B. ∠2=∠3C. ∠2≈∠3D. ∠2 and ∠3 are not supplementary.
Accepted Solution
A:
Answer:Option B is correct[tex]\angle 2 = \angle 3[/tex]Step-by-step explanation:Given that:[tex]\angle 1[/tex] and [tex]\angle 2[/tex] are supplementary.prove that: [tex]a || b[/tex]It is given that:[tex]\angle 1[/tex] and [tex]\angle 2[/tex] are supplementary.By definition of supplementary⇒[tex]\angle 1+ \angle 2 =180^{\circ}[/tex] .....[1]From the figure, you can see that:[tex]\angle 1[/tex] and [tex]\angle 3[/tex] are also supplementary.⇒[tex]\angle 1+ \angle 3 =180^{\circ}[/tex] .....[2]By [1] and [2] we have;⇒[tex]\angle 1+ \angle 2=\angle 1+ \angle 3[/tex]Simplify:[tex]\angle 2 = \angle 3[/tex]Since ∠2 and ∠3 are corresponding angles.Corresponding angles states when the two lines are parallel, then Corresponding Angles are equal and vice versa.by definition we have;[tex]a || b[/tex] proved!