Angela Martine was a female Human Starfleet enlisted crewmember in the 23rd century. She served in the command division aboard the USS Enterprise from 2266 to 2267 under the command of Captain James T. Kirk, during the historic five-year mission.
In 2266, she was assigned to the forward phaser control room as a phaser gun crewmember. As she was about to marry Robert Tomlinson, the Enterprise received a distress call from one of the Earth outposts guarding the Romulan 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 in the first landing party to the Shore Leave Planet. She and Esteban Rodriguez were assigned a specimen survey. After completing the survey, Kirk informed them that once they had beamed the survey to Spock on the Enterprise, they could enjoy themselves on the planet. As they enjoyed themselves, they found themselves briefly trapped by a tiger. After escaping from the tiger, they were strafed by a Japanese Zero. Presuming Angela dead, Rodriguez left 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")
Background information Edit
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 was sometimes quoted as "Angela Martine-Teller," with a hyphenated last name.
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 was unknown if the name was changed to "Angela Martine" during the filming. 
One interesting point about Martine's background was that she might 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.