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The problem involves solving for \( x \) in a triangle, where the angles are given as follows:

- One angle is \( 60^\circ \),
- One angle is a right angle ( \( 90^\circ \) ),
- The third angle is \( (3x - 12)^\circ \).

We know that the sum of the interior angles of a triangle is always \( 180^\circ \). Therefore, we can set up the equation:

\[
60^\circ + 90^\circ + (3x - 12)^\circ = 180^\circ
\]

Simplifying this equation:

\[
150^\circ + (3x - 12)^\circ = 180^\circ
\]

\[
3x - 12 = 180^\circ - 150^\circ
\]

\[
3x - 12 = 30^\circ
\]

Now, add \( 12 \) to both sides:

\[
3x = 42^\circ
\]

Finally, divide by 3:

\[
x = 14^\circ
\]

So, the value of \( x \) is \( 14 \).

Would you like a more detailed explanation or have any other questions?

Here are five questions to deepen your understanding:
1. What is the sum of the angles in a triangle?
2. How does knowing one angle in a right triangle help solve for the others?
3. Can you use this method to solve for angles in non-right triangles?
4. What are other common equations involving angles in geometry?
5. How can algebraic expressions like \( 3x - 12 \) be used to represent angles?

**Tip:** Always remember that the sum of the interior angles in a triangle is \( 180^\circ \), which is helpful for solving many geometry problems.

The measures of the angles of a triangle are shown in the figure below. Solve for x. The angles are 60°, (3x - 12)°, and a right angle (90°).

This problem involves solving for x in a triangle where one angle is 60°, another is (3x - 12)°, and a right angle. Using the angle sum theorem, learn how to set up and solve the equation. Suitable for students in Grades 8-10.

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