Two angles are given, the sides of which are parallel. One of them is 70 degrees larger than the second. Find every corner.

If the sides of one corner are parallel to the sides of the other, then these angles are either equal or add up to 180 degrees. Indeed, this can be proved by drawing the corresponding side parallel to each side, and then either turn the angle in the other direction, or in the same direction.
In our case, the angles look in different directions, since they are not equal, which means they add up to 180 degrees.
Let one of the angles be x, then the second is x + 70.
Let’s make the equation:
x + (x + 70) = 180.
2x = 110.
x = 55.
The first angle is 55 degrees, the second 55 + 70 = 125 degrees.