Given:
- An isosceles glass prism.
- One face of the prism is coated with silver.
- A ray of light is incident normally on the other face, which is equal to the silvered face.
- The ray of light is reflected twice on the same sized faces.
- The ray of light emerges through the base of the prism perpendicularly.

To find:
- The angles of the prism.

Solution:

Step 1: Understanding the problem
- We have an isosceles glass prism with one face coated with silver.
- A ray of light is incident normally on the other face, which is equal to the silvered face.
- The ray of light undergoes two reflections on the same sized faces.
- Finally, the ray emerges through the base of the prism perpendicularly.

Step 2: Analyzing the situation
- Since the ray of light is incident normally on the face of the prism, it will not deviate from its path initially.
- After the first reflection, the ray of light will deviate from its original path and change direction.
- After the second reflection, the ray of light will again change direction and emerge through the base of the prism perpendicularly.

Step 3: Understanding the properties of an isosceles prism
- An isosceles prism has two equal angles opposite to the equal sides.
- The angles between the base and the equal sides are equal.
- The angles between the faces of the prism are equal.

Step 4: Determining the angles of the prism
- Let the angles of the prism be A, A, and B.
- The angle between the two equal sides of the prism is A.
- The angle between the base and the equal sides is B.
- After the first reflection, the ray of light will be incident normally on the second face. Therefore, the angle of incidence is 90 degrees.
- The angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is also 90 degrees.
- The sum of the angles of incidence and reflection is equal to the angle between the faces of the prism. Therefore, 90 + 90 = 180 degrees = 2A.
- Since the prism is isosceles, the angle between the base and the equal sides is equal to A.
- After the second reflection, the ray of light will emerge through the base of the prism perpendicularly. Therefore, the angle of emergence is 90 degrees.
- The angle of emergence is equal to the angle of incidence. Therefore, the angle of incidence is also 90 degrees.
- The sum of the angles of incidence and emergence is equal to the angle between the faces of the prism. Therefore, 90 + 90 = 180 degrees = 2A.
- From the above two equations, we can conclude that A = 90 degrees and B = 90 degrees.

Step 5: Final answer
- The angles of the prism are 90 degrees, 90 degrees, and 90 degrees.

Conclusion:
- The angles of the prism are 90 degrees, 90 degrees, and 90 degrees.