Answer :
Answer:
Given the statement:
Lines a and b are parallel and lines e and f are parallel.
if [tex]m \angle 1 = 89^{\circ}[/tex]
By supplementary angles:
[tex]m\angle 1+ m\angle 2 = 180^{\circ}[/tex]
⇒[tex]89^{\circ}+ m\angle 2 = 180^{\circ}[/tex]
Subtract 89 degree from both sides we have;
[tex]m \angle 2 = 91^{\circ}[/tex]
Since,
m∠4 = m∠5 [Vertically Opposite angles] .....[1]
m∠4 = m∠3 [Alternate Interior angle] .....[2]
By [1] and [2] we have;
m∠5 =m∠3 ....[3]
Also;
m∠2 = m∠3 [Alternate interior angle] ....[4]
by [3] and [4] we have;
m∠5 = m∠2
Substitute the given values we have;
[tex]m \angle 5 = 91^{\circ}[/tex]
Therefore, the measure of [tex]m \angle 5[/tex] is, [tex]91^{\circ}[/tex]
