Answer:
The complete demonstration would be
We know that line m and line n are parallel, also [tex]m\angle1=50[/tex] and [tex]m\angle1=48[/tex], line s bisects [tex]\angle ABC[/tex].
Now, by angle addition postulate we know that [tex]\angle[/tex]DEF=[tex]m\angle1+m\angle2=50+48=98[/tex]
Then, by alternate exterior angle [tex]\angle[/tex]DEF[tex]\cong \angle ABC[/tex], because alternate exterior angles are always congruent.
So, by definition of bisector Angles 4 and 5 are congruent, because a bisector line divides the angle in two equal parts.
[tex]m\angle 4=m\angle 5=\frac{98}{2}=49[/tex]
Then, we see that angle 3 and angle 4 are vertical angles, and the congruence postulate states that vertical angles are always congruent. So, by substitution we have
[tex]m\angle 3=49[/tex]
