In the given triangle we have the following:
A. The sum of the inner angles of a triangle is always equal to 180, that is:
[tex]\angle1+\angle2+\angle3=180[/tex]
From this, we can solve for the sum of angles 1 and 2 and we get:
[tex]\angle1+\angle2=180-\angle3[/tex]
Now, we also know that angles 3 and 4 are supplementary angles and therefore their sum is 180 degrees, that is:
[tex]\angle4+\angle3=180[/tex]
Solving for angle 4:
[tex]\angle4=180-\angle3[/tex]
Equating both results we get:
[tex]\angle1+\angle2=\angle4[/tex]
Therefore, it is true that angle 4 is the sum of angles 1 and 2.
B. We have that the sum of angles 2 and 3 is:
[tex]\angle2+\angle3=180-\angle1[/tex]
If this were equal to angle 4 we would have:
[tex]\begin{gathered} \angle4=180-\angle1 \\ \angle4+\angle1=180 \end{gathered}[/tex]
B
