The difference of the same side interior angles of two parallel lines is 50°. Find the measures of these two angles.

Answer: ______ &______

115 and 65 degrees

Let's denote the two same side interior angles as x and y.

According to the given information, the difference between these two angles is 50 degrees.

Therefore, we can set up the equation:

x - y = 50

Since these two angles are corresponding angles, and corresponding angles formed by a transversal cutting two parallel lines are congruent, we can also set up the equation:

x = y

Now we can substitute x = y into the first equation:

x - x = 50

0 = 50

This equation is inconsistent, meaning there is no solution that satisfies both equations.

Therefore, there are no measures of these two angles that satisfy the given conditions.

To find the measures of the two angles, we need to use the properties of parallel lines and same side interior angles.

Let's start by labeling the angles. Let's call one angle x and the other angle y.

Given that the difference between the same side interior angles is 50°, we can write the equation:

x - y = 50°

Since the lines are parallel, we know that same side interior angles are congruent. Therefore, we can also write:

x = y

Now we have a system of equations:

x - y = 50°
x = y

Solving the system of equations, we can substitute x with y in the first equation:

y - y = 50°
0 = 50°

This equation has no solution, which means there are no measures for the angles that satisfy the given conditions.

Therefore, there is no answer to this question.

they add to 180º