Question

Fill in the blank for the missing reason in the flow proof.

Answer 1

Given:
`m \angle 5 = 40^\circ` ,
`m \angle 2 = 140^\circ`

To prove:
`a\parallel b`

Proof:

a)
`m \angle 5 = 40^\circ`

Reason: Given

b)
`m \angle 2 = 140^\circ`

Reason: Given

c)
`\angle2, \angle 5` are supplementary angles.

Reason: As,
`m \angle 2+ m \angle 5` =
`40^\circ+ 140^\circ = 180^\circ`. since, the measures of angles 2 and 5 is 180 degrees, So, they are supplementary angles.

d)
`\angle2, \angle 5` are same side interior angles.

Reason: Angle 2 and 5 are formed on the same side of the transversal. Hence, they are same side interior angles.

e)
`a \parallel b`

Reason: As angles 2 and 5 are formed on the same side of the transversal and these angles are supplementary angles. So, line 'a' is parallel to 'b'.