The figure below shows a circle with center \( E \) and diameter \( \overline{X G} \). Which of the angles must be right angles? Select all that apply.

In a circle, any angle inscribed with its vertex on the circle and whose sides are formed by the endpoints of a diameter is a right angle. Therefore, if the diameter is \( \overline{X G} \) and \( E \) is the center, any angle formed by \( X \) or \( G \) and any other point on the circle (let's say \( P \)) must be a right angle (i.e., \( \angle X P G \) is a right angle). Additionally, if you have triangles formed with the diameter as one side and the other vertices on the circumference, those angles opposite the diameter will also always be right angles due to the inscribed angle theorem. So, if you see angles directly related to that diameter, you should consider them as right angles!