Find the measure of an angle which is
(i) equal to its complement, (ii) equal to its supplement.

Answer

To solve the question of finding the measure of an angle that is equal to its complement and another angle that is equal to its supplement, we can break it down into two parts.

### Part (i): Angle equal to its complement

1. **Define the angle**: Let the angle be \( x \).
2. **Define the complement**: The complement of \( x \) is given by \( 90 - x \).
3. **Set up the equation**: Since the angle is equal to its complement, we can write the equation:
\[ x = 90 - x \]
4. **Solve for \( x \)**: Add \( x \) to both sides:
\[ x + x = 90 \]
This simplifies to:
\[ 2x = 90 \]
5. **Divide by 2**: To find \( x \), divide both sides by 2:
\[ x = \frac{90}{2} = 45 \]
6. **Conclusion**: The angle that is equal to its complement is \( 45^\circ \).

### Part (ii): Angle equal to its supplement

1. **Define the angle**: Let the angle be \( y \).
2. **Define the supplement**: The supplement of \( y \) is given by \( 180 - y \).
3. **Set up the equation**: Since the angle is equal to its supplement, we can write the equation:
\[ y = 180 - y \]
4. **Solve for \( y \)**: Add \( y \) to both sides:
\[ y + y = 180 \]
This simplifies to:
\[ 2y = 180 \]
5. **Divide by 2**: To find \( y \), divide both sides by 2:
\[ y = \frac{180}{2} = 90 \]
6. **Conclusion**: The angle that is equal to its supplement is \( 90^\circ \).

### Final Answers:
- (i) The angle equal to its complement is \( 45^\circ \).
- (ii) The angle equal to its supplement is \( 90^\circ \).