Let's carefully analyze what happens to the measure of an angle when one of its arms is extended.
To understand this, consider an angle formed by two rays (or arms) originating from a common point called the vertex. The measure of an angle is determined by the rotation required to move one arm to the position of the other around the vertex.
Key points to consider:
1. The measure of an angle is a geometrical property that depends on the relative positions of the two arms.
2. Extending an arm means making one of the rays longer but continuing in the same direction.
3. This extension does not change the relative positions of the arms or the rotation around the vertex.
Given these points, extending one arm does not alter the angle's measure because:
- The angle's measure depends solely on the direction of the arms, not their lengths.
- Extending an arm keeps the direction of the arm unchanged, thereby keeping the angle measure unchanged.
Thus, when an arm of an angle is extended, the measure of the angle:
c. remains the same
