To find the supplementary angle of an interior angle, you subtract the measure of that interior angle from 180 degrees.
Understanding Supplementary Angles
Supplementary angles are a pair of angles that add up to 180 degrees. Think of them forming a straight line when placed adjacent to each other. The reference clarifies this: "Two angles are said to be supplementary angles if they add up to 180 degrees."
The Formula
Based on the definition, finding a supplementary angle is straightforward. The supplementary angle to any given angle (including an interior angle) is determined by a simple calculation. The reference states: "The supplementary angle to any angle is 180 degrees minus that angle."
So, the formula is:
- Supplementary Angle = 180° - Interior Angle
This principle holds true for any interior angle, whether it's part of a polygon or any other figure, as long as you know its measure.
Practical Examples
Let's look at a few examples to see this formula in action.
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Example 1: An Interior Angle of 60°
- Supplementary Angle = 180° - 60°
- Supplementary Angle = 120°
- Check: 60° + 120° = 180°
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Example 2: An Interior Angle of 105°
- Supplementary Angle = 180° - 105°
- Supplementary Angle = 75°
- Check: 105° + 75° = 180°
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Example 3: An Interior Angle of a Square (90°)
- Supplementary Angle = 180° - 90°
- Supplementary Angle = 90°
- Check: 90° + 90° = 180°
You can visualize this relationship easily. If you extend one side of a polygon at a vertex, the interior angle and the exterior angle at that vertex form a linear pair, which are supplementary angles.
Quick Reference Table
| Interior Angle (Degrees) | Calculation | Supplementary Angle (Degrees) |
|---|---|---|
| 30 | 180 - 30 | 150 |
| 45 | 180 - 45 | 135 |
| 90 | 180 - 90 | 90 |
| 120 | 180 - 120 | 60 |
| 150 | 180 - 150 | 30 |
To summarize, finding the supplementary angle of an interior angle requires only knowing the measure of the interior angle and subtracting it from 180 degrees.
