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The problem asks for the value of \( x \) based on the diagram provided. The diagram shows an angle split into two smaller angles: one labeled \( x^\circ \) and the other labeled \( 2x^\circ - 12^\circ \). These two angles are part of a straight angle (which sums up to \( 180^\circ \)).

To solve for \( x \), we can set up the equation:

\[
x + (2x - 12) = 90
\]

This is because the two angles form a right angle (90 degrees).

Simplify the equation:

\[
x + 2x - 12 = 90
\]

\[
3x - 12 = 90
\]

Add 12 to both sides:

\[
3x = 102
\]

Now, divide by 3:

\[
x = 34
\]

Thus, the value of \( x \) is 34, which matches option 5.

Would you like a further explanation, or do you have any questions?

Here are some related questions:
1. How do you solve for \( x \) when dealing with complementary and supplementary angles?
2. What is the sum of angles on a straight line, and how can this help in solving similar problems?
3. Can you explain how to approach problems involving multiple angle equations?
4. How do properties of adjacent angles help in solving for unknowns in geometry?
5. What are some common types of angle relationships used in geometry?

**Tip:** Remember that angles on a straight line always sum up to \( 180^\circ \).

This problem involves solving for x in an angle equation, where one angle is x and the other is (2x - 12), forming a linear pair. Learn how to use the Angle Sum Theorem and basic algebra to find the value of x, suitable for Grades 7-10.

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