Question: The difference between twice an angle's measure and its supplement is 27. Find the measure of the angle.
1. **State the problem:** We need to find the measure of an angle given that the difference between twice its measure and its supplement is 27.
2. **Define variables:** Let the angle be $x$ degrees.
3. **Recall the supplement rule:** The supplement of an angle $x$ is $180 - x$ degrees.
4. **Set up the equation:** Twice the angle is $2x$. The difference between twice the angle and its supplement is given as 27, so:
$$2x - (180 - x) = 27$$
5. **Simplify the equation:**
$$2x - 180 + x = 27$$
$$3x - 180 = 27$$
6. **Isolate $x$:**
$$3x = 27 + 180$$
$$3x = 207$$
7. **Divide both sides by 3:**
$$\cancel{3}x = \frac{207}{\cancel{3}}$$
$$x = 69$$
8. **Answer:** The measure of the angle is $69$ degrees.