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'.