1. **State the problem:** We need to find the measure of an angle that is twice the measure of its complement. 2. **Recall the definition:** Two angles are complementary if their measures add up to 90 degrees. 3. **Set variables:** Let the angle be $x$ degrees. Its complement is then $90 - x$ degrees. 4. **Write the equation:** Since the angle is twice its complement, we have: $$x = 2(90 - x)$$ 5. **Solve the equation:** $$x = 180 - 2x$$ 6. **Add $2x$ to both sides:** $$x + 2x = 180$$ $$3x = 180$$ 7. **Divide both sides by 3:** $$\frac{\cancel{3}x}{\cancel{3}} = \frac{180}{3}$$ $$x = 60$$ 8. **Answer:** The angle measures $60$ degrees. 9. **Check:** Its complement is $90 - 60 = 30$ degrees, and $60$ is indeed twice $30$.