If one angle of a linear pair is acute , then its other angle will be ____

Answer

To solve the problem step by step, we need to analyze the properties of angles in a linear pair.

### Step-by-Step Solution:

1. **Understanding Linear Pair**: A linear pair consists of two adjacent angles formed when two lines intersect. The sum of the angles in a linear pair is always 180 degrees.

2. **Define the Angles**: Let’s denote the two angles in the linear pair as angle α (alpha) and angle β (beta). According to the problem, we assume that angle α is the acute angle.

3. **Set Up the Equation**: Since α and β form a linear pair, we can write the equation:
\[ \alpha + \beta = 180^\circ \]

4. **Express β in Terms of α**: Rearranging the equation gives:
\[ \beta = 180^\circ - \alpha \]

5. **Understanding Acute Angles**: An acute angle is defined as an angle that is less than 90 degrees. Therefore, we have:
\[ 0^\circ < \alpha < 90^\circ \]

6. **Substituting α into the Equation for β**: Since α is less than 90 degrees, we can analyze what happens to β:
- If α is less than 90 degrees, then:
\[ \beta = 180^\circ - \alpha > 180^\circ - 90^\circ = 90^\circ \]

7. **Conclusion about β**: This means that β must be greater than 90 degrees. Therefore, β is an obtuse angle.

### Final Answer:
If one angle of a linear pair is acute, then its other angle will be **obtuse**.

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