According to the provided information, the measure of an exterior angle is determined by the sum of the two internal opposite angles in the context described.
Understanding Exterior Angles (Based on the Provided Reference)
Based on the reference given, exterior angles are defined by their position relative to a polygon:
- Location: They lie on the outside of the polygon.
- Relationship to Inner Angles: The reference states that exterior angles are angles that are parallel to the inner angles of a polygon.
- Context Example: In the context of the reference, 'a' and 'b' are given as interior angles, while 'd' is presented as the exterior angle.
Let's organize the angle types mentioned in the reference:
| Angle Type | Description | Example Label (from reference) |
|---|---|---|
| Interior | Inner angles of a polygon | 'a', 'b' |
| Exterior | Angles outside the polygon | 'd' |
Determining the Measure of an Exterior Angle
The reference provides a specific method for determining the measure of an exterior angle in the described context:
- The core principle stated is that "The measure of an exterior angle is equal to the sum of the two internal opposite angles."
In the context provided by the reference, where 'a' and 'b' are internal angles and 'd' is the exterior angle, this means:
- Measure of angle 'd' = Measure of angle 'a' + Measure of angle 'b'
This rule describes how to find the angle of the exterior angle 'd' using the measures of the interior angles 'a' and 'b' that are opposite to it.
Example Calculation
Let's illustrate this rule with a simple example using the angles described:
- Suppose the measure of angle 'a' is 50 degrees.
- Suppose the measure of angle 'b' is 70 degrees.
- According to the reference, the measure of the exterior angle 'd' is the sum of these two internal opposite angles.
- Therefore, the measure of angle 'd' = 50° + 70° = 120 degrees.
This calculation shows how the angle of the exterior angle is determined based on the relationship provided in the reference.
