https://file.aiquickdraw.com/mathbot/file/172618137682089x9ifw6.jpg

The diagram you've uploaded shows various lines intersecting at point \( X \), forming different angles. There are specific angle measures labeled, and the goal seems to be determining the remaining angle values around \( X \).

### Steps to solve:
1. **Angle Sum at a Point:**
   The total of all angles around a point is \( 360^\circ \). So, we can use the given angle measures to find the missing ones.

2. **Given Angles:**
   - Angle \( AXG = 110^\circ \)
   - Angle \( BXC = 50^\circ \)
   - Angle \( CXD = 40^\circ \)
   - Angle \( DXE = 32^\circ \)

### Finding the remaining angle(s):
We need to sum the given angles and subtract from \( 360^\circ \).

- Sum of known angles: 
  \[
  110^\circ + 50^\circ + 40^\circ + 32^\circ = 232^\circ
  \]
- Remaining angle \( FXG \): 
  \[
  360^\circ - 232^\circ = 128^\circ
  \]

Thus, the missing angle \( FXG \) is \( 128^\circ \).

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Would you like further clarification on any part of this solution, or do you need more details on specific angles?

Here are 5 follow-up questions for deeper understanding:
1. How would you verify that all the angles correctly sum up to \( 360^\circ \)?
2. Can you identify any supplementary or complementary angle pairs from the diagram?
3. What does the sum of angles on a straight line add up to, and how can that help solve similar problems?
4. If the lines were parallel, how would the angle relationships change?
5. Can you create a system of equations to solve for missing angles in a similar scenario?

**Tip:** Always check if any lines are parallel or perpendicular, as that can provide helpful geometric relationships to solve for unknown angles.

Solve for the measure of each angle that has X as its vertex. Given angles AXG=110°, BXC=50°, CXD=40°, DXE=32°, find the missing angles around point X.

Learn how to solve for unknown angles around a point, where the total sum of angles is 360°. Using given angle measures like 110°, 50°, 40°, and 32°, find the missing angles in a geometric diagram. Suitable for students in Grades 7-9.

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