Answer:
The value of [tex]m\angle 3-m\angle 1[/tex] = [tex]50^{\circ}[/tex]
Step-by-step explanation:
Vertical Angle theorem: It is about the angles that are opposite to each other.
Also, vertical angle are congruent that means vertical angles are equal.
In the given figure; [tex]m\angle 3[/tex] and [tex]70^{\circ}[/tex] are vertical angle
then, by vertical angle theorem, [tex]m\angle3 =70^{\circ}[/tex].
Supplementary angle: the sum of the angles whose measure on the straight line is 180 degree.
From the figure, [tex]70^{\circ}[/tex] , [tex]\angle 1[/tex] and [tex]m\angle 2 =90^{\circ}[/tex] forms a straight line.
then, by the definition of Supplementary angle;
[tex]70^{\circ}+m\angle 1 +m\angle 2=180^{\circ}[/tex]
Substituting the value of [tex]m\angle 2 =90^{\circ}[/tex] in above equation:
[tex]70^{\circ}+m\angle 1 + 90^{\circ} =180^{\circ}[/tex] or
[tex]160^{\circ}+m\angle 1=180^{\circ}[/tex]
Simplify:
[tex]m\angle 1=180^{\circ}-160^{\circ} =20^{\circ}[/tex]
therefore, [tex]m\angle 1= 20^{\circ}[/tex] and [tex]m\angle 3=70^{\circ}[/tex],
the value of [tex]m\angle3-m\angle1= 70^{\circ}-20^{\circ} =50^{\circ}[/tex].
