Final answer:
The correct completion of the sentence is 'The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles', reflecting the exterior angle theorem in geometry.
Step-by-step explanation:
The sentence to complete is: 'The measure of an exterior angle of a triangle is the sum of the measures of the remote interior angles'. The correct answer from the choices given is A. equal to; two. This is because the measure of any exterior angle of a triangle is always equal to the sum of the measures of the two interior angles that are not adjacent to it (these are known as the remote interior angles).
When thinking of a triangle, it's important to remember that it is a three-sided figure lying on a plane with three angles adding up to 180 degrees. The relationship between the exterior and interior angles of a triangle is fundamental to understanding triangle geometry. An exterior angle is formed by one side of a triangle and the extension of an adjacent side. According to the exterior angle theorem, this exterior angle is equal to the sum of the two non-adjacent (remote) interior angles.