Understanding the Problem
To find the angle that is 5 times its complement, we first need to understand what a complement is. The complement of an angle \( x \) is given by \( 90^\circ - x \).

Setting Up the Equation
Given that the angle is 5 times its complement, we can express this relationship mathematically:
- \( x = 5(90^\circ - x) \)

Solving the Equation
Now, let's solve the equation step by step:
1. **Distribute the 5**:
- \( x = 450^\circ - 5x \)
2. **Combine like terms**:
- Add \( 5x \) to both sides:
- \( x + 5x = 450^\circ \)
- \( 6x = 450^\circ \)
3. **Isolate \( x \)**:
- Divide both sides by 6:
- \( x = \frac{450^\circ}{6} \)
- \( x = 75^\circ \)

Conclusion
The measure of the angle is:
- \( 75^\circ \)
To confirm, we can check the complement:
- **Complement of \( 75^\circ \)**:
- \( 90^\circ - 75^\circ = 15^\circ \)
- **5 times the complement**:
- \( 5 \times 15^\circ = 75^\circ \)
Thus, the solution is verified, and the angle that is 5 times its complement is indeed \( 75^\circ \).