https://file.aiquickdraw.com/mathbot/file/1727467592270t8mdo6q9.jpg

The image presents a geometry problem involving a diagram where angles are given, and we are tasked with finding \( m\angle DGB \). Let's break it down:

### Given Information:
- \( m\angle AGF = 65^\circ \)
- \( m\angle CGE = 88^\circ \)
- The problem is asking us to find \( m\angle DGB \).

### Approach:
- Since \( G \) is the intersection point of two lines, all angles around point \( G \) should sum up to \( 360^\circ \). 
- \( m\angle AGF \), \( m\angle CGE \), and \( m\angle DGB \) are angles at point \( G \), which are part of this sum.
  
We can also notice that \( m\angle DGB \) is a vertically opposite angle to the combined angles \( m\angle AGF \) and \( m\angle CGE \). Thus, we can find \( m\angle DGB \) by subtracting the sum of these two given angles from \( 180^\circ \) (since vertically opposite angles form a linear pair).

### Calculation:
\[
m\angle DGB = 180^\circ - (m\angle AGF + m\angle CGE)
\]
\[
m\angle DGB = 180^\circ - (65^\circ + 88^\circ)
\]
\[
m\angle DGB = 180^\circ - 153^\circ
\]
\[
m\angle DGB = 27^\circ
\]

Thus, \( m\angle DGB = 27^\circ \).

Would you like more details on how this was solved or any further explanation?

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Here are 5 related questions to expand on this topic:
1. How do you identify vertically opposite angles in intersecting lines?
2. What is the sum of angles around a point?
3. Can two angles formed by intersecting lines be supplementary?
4. What other types of angles can be formed by intersecting lines?
5. How can we verify if angles are congruent in a given diagram?

**Tip:** Always remember that vertically opposite angles are equal when two lines intersect.

In the diagram below, m∠AGF = 65° and m∠CGE = 88°. Find m∠DGB.

Learn how to find the angle m∠DGB using the concepts of vertically opposite angles and linear pairs. The problem involves given angles m∠AGF = 65° and m∠CGE = 88° and is suitable for students in Grades 6-8.

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