Which valve is affected with damage to the papillary muscle in the left ventricle

Mitral valve

Explanation:

The mitral valve is a valve that can be located in the heart, more specifically on the left side between the left atrium and the left ventricle. When the left atrium fills up with blood (which has been oxygenated by the lungs), the mitral valve opens to allow the blood to flow into the ventricle.

The papillary muscles are specific to the ventricles of the heart, and those are the muscles that contract the chamber, to move blood to the lungs or to the rest of the body.