1. Given
2. Opposite sides in common rays.
3. Definition of supplementary angles.
4. Substitution
5. Opposite angles are congruent.
6. Substitution
7. Definition of supplementary angles.
It is given to us that [tex]m\angle 3 = m\angle 4 ...(i)[/tex]
Now, and lie on the opposite sides in a common ray.
So, and are supplementary.
Sum of two supplementary angles is .
So, [tex]m\angle 2 + m\angle 3 = 180 ^{\circ} ...(ii)[/tex]
Substitute the value of [tex]m\angle 3[/tex] from [tex](i)[/tex] in [tex](ii)[/tex],
[tex]m\angle 2 + m\angle 4 = 180 ^{\circ} ...(iii)[/tex]
When two lines intersect at a point, the opposite angles are equal.
So, [tex]m\angle 1 = m\angle 4 ...(iv)[/tex]
Substitute the value of [tex]m\angle 4[/tex] in [tex](iii)[/tex]
[tex]m\angle 2 + m\angle 1 = 180 ^{\circ}[/tex]
Since, the sum of these two angles is .
So, by definition of supplementary angles [tex]\angle 1, \angle 2[/tex] are supplementary.
Learn more about supplementary angles here:
https://brainly.com/question/18164299?referrer=searchResults
