In 2266, she was a specialist in fire control, part of a team responsible for operating the ship's phasers. As she was about to marry Robert Tomlinson, the Enterprise received a distress call from one of the Earth outposts guarding the neutral zone. The wedding was postponed. In the course of chasing and crippling the Romulan Bird-of-Prey responsible for the attack, her fiancé inhaled a lethal quantity of phaser coolant. (TOS: "Balance of Terror")
In 2267, she was part of a landing party that visited the Shore Leave Planet. There, she was thought killed by an aircraft that strafed her. In fact, she was taken below the planet's surface where her injuries were repaired; she reappeared during the caretaker's explanation of the planet's function. (TOS: "Shore Leave")
|Communications officers of the starships Enterprise|
|USS Enterprise:||Alden • Farrell • Garison • Hadley • Lisa • M'Ress • Palmer • Uhura|
|ISS Enterprise NX-01:||Sato|
|ISS Enterprise (NCC-1701):||Uhura|
|USS Enterprise (alternate reality):||Hawkins • Uhura|
Angela Martine was portrayed by Barbara Baldavin. In her second appearance, the character was named "Mary Teller" in the script, but when the same actress was cast, the name was changed to Angela. Since she was referred to as "Angela Martine" in one episode and "Angela Teller" in the other, her credit for her later appearances is sometimes quoted as "Angela Martine-Teller," with a hyphenated last name. By "Turnabout Intruder" she was in an operations division uniform, with the rank of lieutenant and was referred to as "Lisa" and credited as communications officer.
Baldavin also appeared in "Space Seed", in a scene which was eventually cut from the finished episode. In the script, the role she played was called "Baker", and it is unknown if the name was changed to "Angela Martine" during the filming. 
One interesting point about Martine's background is that she may be Catholic. During her aborted wedding in "Balance of Terror", she genuflected before the altar. This would be consistent with Star Trek's policy of showing diversity among cultures that were not necessarily popular with the mainstream, a description which Catholicism certainly fit in the 1960s.