A person is not able to extend his metacarpophalangeal joint. Injury to which of the following nerve result in this?

Damage to posterior interosseous nerve result in inability to extend the fingers at the metacarpophalangeal joints and radial detion of the wrist on wrist extension caused by weakness of extensor carpi ulnaris muscle. Posterior interosseous nerve or deep ulnar nerve is a pure motor branch of radial nerve in the forearm. It supplies the extensor muscles of forearm including the extensor carpi ulnaris. Ulnar nerve palsy result in loss of fine intrinsic motions of hand. It result in an abduction deformity of the little finger from paralysis of the interossei, interosseous muscle wasting, and paial claw hand from interphalangeal flexion deformities of the ring and little fingers. Radial nerve injury result in wrist drop. Axillary or proximal injury result in triceps weakness in addition to wrist drop. Injury in the axilla causes damage to triceps brachii, anconeus, brachioradialis and extensor carpi radialis longus. Ref: Neurology in Clinical Practice: The neurological disorders, Volume 2 edited by Walter George Bradley page 2315. LeBlond R.F., DeGowin R.L., Brown D.D. (2009). Chapter 14. The Neurologic Examination. In R.F. LeBlond, R.L. DeGowin, D.D. Brown (Eds), DeGowin's Diagnostic Examination, 9e.