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To solve for \( m \angle x \) in the given figure, we need to use the properties of angles and supplementary angles. Let's break it down step-by-step:

### Step 1: Identify the relationship between angles
- The two angles labeled 101° and 119° are on a straight line, meaning they are supplementary (their sum must be 180°).
- Similarly, the angle \( x \) and the adjacent angle (58°) are on a straight line, meaning they are also supplementary.

### Step 2: Apply the supplementary angle rule
- For the 101° and 119° angles:  
  Since \( 101^\circ + 119^\circ = 220^\circ \), the sum exceeds 180°. This shows they are in different parts of the figure and don’t directly affect the calculations for angle \( x \).

- Now, consider \( \angle x \) and 58°. These are supplementary angles:
  \[
  m \angle x + 58^\circ = 180^\circ
  \]
  Therefore:
  \[
  m \angle x = 180^\circ - 58^\circ = 122^\circ
  \]

However, based on the choices, this suggests we may need to adjust our interpretation, as this directly doesn't match the options. Let's check carefully if this matches with the geometry surrounding \( \angle x \).

It appears we need to evaluate \( \angle x = 133 \ ans% ;

What is m∠x in the figure below? (involving angles 58°, 61°, 101°, and 119°)

Learn how to solve for m∠x in a geometric figure by applying the Supplementary Angle Theorem. This problem involves identifying angle relationships and using basic geometry rules. Suitable for students in Grades 8-10.

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