Answer:
Given: [tex]\angle 1[/tex], [tex]\angle 2[/tex], [tex]\angle 3[/tex], [tex]\angle 4[/tex] formed by two intersecting segments.
In the given figure;
Linear pair states that a pair adjacent angle formed when two lines intersect.
Then by definition of linear pairs,
[tex]\angle 1[/tex] and [tex]\angle 2[/tex] forms a linear pair
Also, [tex]\angle 2[/tex] and [tex]\angle 3[/tex] forms a linear pair.
Linear pair postulates states that the two angle that forms a linear pair are supplementary(i,e add up to 180 degree).
Then by linear pair postulates;
[tex]m\angle 1+ m\angle 2 =180^{\circ}[/tex]
and
[tex]m\angle 2+m \angle 3 =180^{\circ}[/tex]
Substitution property of equality states that if x =y then, x can be substituted in for y or vice -versa.
then by substitution property of equality:
[tex]m\angle 1+m\angle 2=m\angle 2+ m\angle 3[/tex]
Addition property of equality states that:
if x =y, then x + z = y+ z
By addition property of equality:
[tex]m\angle 1 =m\angle 3[/tex] hence proved!
