Explanation:
When an arm of an angle is extended, the measure of the angle remains the same.

Reasoning:
To understand why the measure of an angle remains the same when one of its arms is extended, let's consider the definition of an angle.

Definition of an angle:
An angle is formed by two rays or line segments that share a common endpoint, called the vertex of the angle. The two rays or line segments that form the angle are called the arms of the angle.

Effect of extending an arm:
When one of the arms of an angle is extended, the angle itself does not change. The extended arm simply continues in a straight line beyond the vertex. This means that the measure of the angle, which is determined by the opening between the two arms, remains the same.

Example:
For example, let's consider a 90-degree angle (a right angle) formed by two rays or line segments AB and BC, with B as the vertex. If we extend the arm AB, the angle still remains a right angle, even though the length of the arm AB has increased. The measure of the angle remains 90 degrees.

Visual representation:
To visually understand this concept, you can draw angles on a piece of paper using a protractor. Extend one arm of the angle and measure the angle again. You will observe that the measure of the angle remains the same.

In conclusion:
When an arm of an angle is extended, the measure of the angle remains the same. The extension of the arm does not affect the opening between the arms, which determines the measure of the angle.