https://file.aiquickdraw.com/mathbot/file/1725387915878cyzacvv1.jpg

Let's analyze the problem step by step based on the given diagram.

### Given:
- \( m \angle CIH = 99^\circ \)
- \( m \angle BGD = 34^\circ \)
- We need to find \( m \angle PHG \).

### Approach:

1. **Identify Key Angles:**
   - In the diagram, angles are positioned at various intersecting lines.
   - \( \angle CIH \) is given as 99°, and \( \angle BGD \) is 34°.

2. **Observe the Geometry:**
   - The line \( AB \) intersects the lines \( CH \) and \( DE \), forming angles at points \( G \) and \( H \).
   - Angle \( \angle PHG \) appears to be formed by the extension of one line and the intersection of two others.

3. **Relationships between Angles:**
   - Use properties such as vertical angles, linear pairs, or corresponding angles to relate these angles and solve for \( m \angle PHG \).

4. **Calculations:**
   - \( m \angle CIH = 99^\circ \) indicates that the angle opposite to it (likely at point \( P \)) could be calculated using angle relationships like supplementary or vertically opposite angles.
   - \( m \angle BGD = 34^\circ \) could provide additional information on corresponding or adjacent angles.

Let me solve this and provide you with the final answer.

### Solution:

Given that \( m \angle CIH = 99^\circ \) and \( m \angle BGD = 34^\circ \), and the angles are vertically opposite, the corresponding \( m \angle PHG \) is calculated based on the geometry.

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The measure of \( m \angle PHG \) is **47°**.

Would you like a more detailed breakdown of the solution or have any questions?

### Related Questions:
1. How do we calculate vertically opposite angles in such diagrams?
2. What properties of parallel lines are used in angle calculations?
3. How can supplementary angles help solve similar problems?
4. What is the significance of linear pairs in intersecting lines?
5. Can this method be applied to triangles and other polygons?

### Tip:
Always label your angles and lines carefully in a diagram to avoid confusion when applying geometric properties.

In the diagram below, m∠CIH = 99° and m∠BGD = 34°. Find m∠PHG.

This problem involves finding the measure of angle PHG given two other angles in the diagram. Key concepts include vertically opposite angles and linear pairs, making this a suitable exercise for students in Grades 8-10.

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