In this situation, the electromagnetic waves that can be used to help Monica take photographs of the monument despite the smoke-filled surroundings are infrared waves.

- Infrared waves:
Infrared waves are a type of electromagnetic radiation that have longer wavelengths than visible light. These waves are invisible to the human eye but can be detected by specialized cameras and equipment.

- Why infrared waves are suitable for this situation:
1. Penetration through smoke: Infrared waves have the ability to penetrate through smoke and other particles in the air more effectively than visible light. This allows the camera or equipment to capture images with less interference from the smoke-filled surroundings, resulting in clearer photographs of the monument.

2. Lack of interference: Unlike X-rays, gamma rays, and ultraviolet rays, infrared waves do not cause harmful effects or interfere with the human body or the monument itself. They are generally considered safe and non-destructive, making them a suitable choice for photography in this situation.

3. Heat detection: Infrared waves are also commonly used for thermal imaging and heat detection. They can capture the heat signatures of objects, which can be useful in identifying temperature variations and locating objects within the smoke-filled surroundings. This can aid Monica in capturing unique and interesting photographs of the monument, even in the presence of smoke.

- Other electromagnetic waves:
1. X-rays and gamma rays: These waves have much shorter wavelengths and higher energy levels than visible light. They are primarily used in medical imaging and industrial applications. However, they are not suitable for photographing a monument in a smoke-filled environment as they are highly ionizing and can be harmful to living organisms. They also do not provide any advantage in terms of visibility through smoke.

2. Ultraviolet rays: Ultraviolet rays have shorter wavelengths than visible light and are commonly used in forensics, astronomy, and sterilization. However, they are not ideal for photographing in smoky environments as they can be scattered and absorbed by smoke particles, resulting in poor image quality.

In conclusion, infrared waves are the most suitable choice for Monica to overcome the challenge of smoke-filled surroundings while photographing the monument. They can penetrate through smoke, do not cause harm or interference, and can even detect heat signatures, enhancing the photographic possibilities in this situation.