https://file.aiquickdraw.com/mathbot/file/1725598311413z4t3lu07.jpg

Let's go through the problems you've asked about from the image.

### Problem 10:  
"Are \( \angle 1 \) and \( \angle 2 \) supplementary?"

**Solution:**  
Angles are supplementary when their sum is \(180^\circ\). Without the diagram fully visible, I assume the problem mentions that \( \angle 1 \) and \( \angle 2 \) form a linear pair or are adjacent on a straight line. If that's the case, then their sum would indeed be \(180^\circ\). Thus, \( \angle 1 \) and \( \angle 2 \) are **supplementary**.

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### Problem 16:  
"Is \( \angle J \cong \angle D \)?"

**Solution:**  
To determine whether two angles are congruent, we need to know if they have the same measure. From the diagram, \( \angle J \) and \( \angle D \) appear to be vertical angles, which are always congruent. Thus, \( \angle J \cong \angle D \).

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### Problem 18:  
"Is \( m\angle JCA = m\angle DCA \)?"

**Solution:**  
From the given labeling, \( JCA \) and \( DCA \) share the vertex \( C \) and both lie along the same straight line. These two angles would likely form a linear pair, but since they lie on opposite sides of the transversal line, they are vertical angles, which means they are congruent. Therefore, \( m\angle JCA = m\angle DCA \).

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### Problem 20:  
"Is \( \overline{AJ} \cong \overline{AD} \)?"

**Solution:**  
To determine whether two segments are congruent, their lengths must be equal. From the problem, it suggests that these two segments may be equal, possibly because of symmetry in the diagram or a midpoint at \( A \). If this is the case, then \( \overline{AJ} \cong \overline{AD} \).

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### Problem 22:  
"Are \( \angle JAE \) and \( \angle EAF \) adjacent and supplementary?"

**Solution:**  
Adjacent angles share a common side and vertex. Based on the diagram, \( \angle JAE \) and \( \angle EAF \) seem to share the side \( AE \), and they are next to each other. If they also form a straight line together, their measures would add up to \(180^\circ\), making them supplementary. So, they are **adjacent and supplementary**.

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Do you have any questions about the solutions? Here are five follow-up questions that expand on this information:

1. What is the relationship between complementary and supplementary angles?
2. Can vertical angles ever be supplementary? Why or why not?
3. How can we determine if two line segments are congruent without measuring them?
4. What is the sum of the angles in a triangle?
5. How can we prove two angles are congruent using parallel lines and a transversal?

### Tip:
When working with diagrams, always look for relationships like vertical angles, linear pairs, and parallel lines, as these often provide shortcuts to determining angle measures.

Solve problems 10, 16, 18, 20, 22 from the math exercise.

Solve angle relationship problems from a geometry exercise, including supplementary angles, vertical angles, and linear pairs. The problems involve key geometry concepts like congruence and supplementary relationships. Suitable for Grade 8-10 students.

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