How can you be certain that the angles you have created from a square inside the circle?

To confirm that the angles created from a square inscribed in a circle are right angles, you can use the properties of a circle and a square. Each vertex of the square touches the circumference of the circle, and since each side of the square is equal and parallel to the opposite side, the angles formed at each vertex must be 90 degrees. Additionally, applying the Pythagorean theorem or observing that the diagonals of the square bisect each other at right angles further verifies that the angles are indeed right angles. Thus, the geometric relationships ensure the angles are correct.