Finding the linear pair of an angle often involves determining the measure of an adjacent angle that, when combined with the given angle, forms a straight line (180°). The question would be better phrased as "How do you find the measure of the angle that forms a linear pair with a given angle?". Here's how:
A linear pair is a pair of adjacent angles formed when two lines intersect. The angles in a linear pair are supplementary, meaning they add up to 180 degrees.
Here's a step-by-step approach:
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Understand the Definition: Remember that angles in a linear pair are supplementary; therefore, their measures add up to 180°.
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Identify the Given Angle: Let's say you're given an angle 'a'.
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Use the Supplementary Property: To find the angle 'b' that forms a linear pair with 'a', use the equation:
∠a + ∠b = 180°
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Solve for the Unknown Angle: Rearrange the equation to solve for 'b':
∠b = 180° - ∠a
Example
Let's say you have an angle ∠a = 90°. To find the angle ∠b that forms a linear pair with it, you would do the following, as shown in the provided reference:
- Start with the Supplementary Angle Property: ∠a + ∠b = 180°
- Substitute the Known Angle: 90° + ∠b = 180°
- Solve for the Unknown Angle: ∠b = 180° - 90° = 90°
Therefore, the angle that forms a linear pair with a 90° angle is also a 90° angle.
Table: Finding the Linear Pair
| Step | Description | Example (∠a = 60°) |
|---|---|---|
| 1. Identify ∠a | The measure of the given angle. | ∠a = 60° |
| 2. Apply Supplement | Use the property: ∠a + ∠b = 180° | 60° + ∠b = 180° |
| 3. Solve for ∠b | Isolate ∠b: ∠b = 180° - ∠a | ∠b = 180° - 60° = 120° |
| 4. The Linear Pair | ∠b is the angle that forms a linear pair with ∠a. | ∠b = 120° forms a linear pair with 60° |
