Given: [tex]m \angle 5 = 40^\circ[/tex] , [tex]m \angle 2 = 140^\circ[/tex]
To prove: [tex]a\parallel b[/tex]
Proof:
a) [tex]m \angle 5 = 40^\circ[/tex]
Reason: Given
b) [tex]m \angle 2 = 140^\circ[/tex]
Reason: Given
c) [tex]\angle2, \angle 5[/tex] are supplementary angles.
Reason: As, [tex]m \angle 2+ m \angle 5[/tex] = [tex]40^\circ+ 140^\circ = 180^\circ[/tex]. since, the measures of angles 2 and 5 is 180 degrees, So, they are supplementary angles.
d) [tex]\angle2, \angle 5[/tex] 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) [tex]a \parallel b[/tex]
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'.
