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!
Answer:
From the figure it i obvious that angle 2 and angle 3 are equal so option C is correct.
