When two parallel lines are crossed by a transversal, the same side interior angles are supplementary, meaning they add up to 180 degrees.
Let's define the two angles as \( x \) and \( y \), where:
- \( x - y = 50 \) (the difference of the angles)
- \( x + y = 180 \) (the sum of the angles)
Now, we can solve these two equations.
From the first equation, we can express \( x \) in terms of \( y \):
\[ x = y + 50 \]
Now we can substitute this expression for \( x \) in the second equation:
\[ (y + 50) + y = 180 \]
Simplifying this gives:
\[ 2y + 50 = 180 \]
Subtracting 50 from both sides:
\[ 2y = 130 \]
Dividing by 2:
\[ y = 65 \]
Now, substituting \( y \) back into the equation for \( x \):
\[ x = y + 50 = 65 + 50 = 115 \]
Thus, the two angles are:
- \( x = 115^\circ \)
- \( y = 65^\circ \)
Therefore, the angles are \( 115 \) degrees and \( 65 \) degrees.