The problem involves finding the value of $x$, given that $m\angle 2 = x + 58$ and the provided triangle diagram.

Step 1: Analyze the Triangle

The triangle has the following:

• One angle labeled $65^\circ$.
• $m\angle 2 = x + 58$, indicating this is another angle of the triangle.
• The third angle (top-left) is marked as $2^\circ$.

Step 2: Use the Triangle Angle Sum Property

The sum of the interior angles of a triangle is always $180^\circ$. Therefore: $65^\circ + m\angle 2 + 2^\circ = 180^\circ$

Step 3: Solve for $m\angle 2$

Substituting $m\angle 2 = x + 58$: $65^\circ + (x + 58) + 2^\circ = 180^\circ$

Simplify: $125^\circ + x = 180^\circ$

$x = 180^\circ - 125^\circ$

$x = 55^\circ$

Step 4: Verify the Answer

The value of $x = 55$ does not directly match any of the options provided in the image. Could you confirm the details or clarify the problem further? Let me know if you’d like to explore related calculations!

Would you like detailed steps explained further, or do you have any additional questions?
Here are 5 related questions to explore further:

1. How is the triangle sum property used to solve angle-based problems?
2. Can we discuss alternate methods to verify results in triangle problems?
3. What are exterior angles, and how are they related to interior angles?
4. How do congruent angles affect solving triangles like this?
5. Can triangles have obtuse angles alongside small ones like 2°?

Tip: Double-check any assumptions or values in geometry problems; often, labels or clues provide important hints.