Let's denote the angle by $x$ (in degrees).

Step 1: Define the supplement and complement

• The supplement of an angle $x$ is $180^\circ - x$.
• The complement of an angle $x$ is $90^\circ - x$.

Step 2: Translate the problem into an equation

The problem states that the supplement of the angle contains 12 degrees more than twice the complement of the angle. Mathematically, this can be written as:

$180^\circ - x = 2(90^\circ - x) + 12^\circ$

Step 3: Solve the equation

First, expand the right-hand side:

$180^\circ - x = 180^\circ - 2x + 12^\circ$

Simplify and combine like terms:

$180^\circ - x = 192^\circ - 2x$

Now, move the terms involving $x$ to one side of the equation:

$x = 192^\circ - 180^\circ$

Simplify:

$x = 12^\circ$

Step 4: Conclusion

The angle is $12^\circ$.

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Would you like more details or further clarification on the steps?

Here are 5 related questions to deepen your understanding:

1. What happens if the angle's supplement is 5 degrees more than twice its complement?
2. How can you generalize the formula for an angle whose supplement differs from a multiple of its complement by a constant?
3. If the angle were larger than 90°, how would the equation change?
4. How do the concepts of supplement and complement relate to each other geometrically?
5. What if the problem involved a different relationship, such as the supplement being equal to the complement?

Tip: When solving word problems involving angles, always define variables clearly and translate the relationships into algebraic equations step by step.