Answer:
The correct option is a.
Step-by-step explanation:
Given: ∠1 and ∠2 are supplementary angles.
Prove: l║m
Proof:
It is given that ∠1 and ∠2 are supplementary angles.
[tex]\angle 1+\angle 2=180^{\circ}[/tex] .... (1)
∠1 and ∠3 are supplementary angles because both angles lie on a straight line.
[tex]\angle 1+\angle 3=180^{\circ}[/tex] .... (2)
Using (1) and (2), we get
[tex]\angle 1+\angle 2=\angle 1+\angle 3[/tex]
Subtract angle 1 from both the sides.
[tex]\angle 2=\angle 3[/tex]
[tex]\angle 2\cong \angle 3[/tex]
Since ∠2 ≅ ∠3 are corresponding angles,
[tex]l\parallel m[/tex]
Hence proved.
Therefore the missing statement is [tex]\angle 2=\angle 3[/tex] and option a is correct.
