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Let's analyze and solve the questions in the provided worksheet.

### Part 1: Determining if angles are complementary, supplementary, or neither.
1. \( m \angle 1 = 63^\circ \) and \( m \angle 2 = 27^\circ \)
   - Complementary angles sum to \( 90^\circ \).
   - \( 63^\circ + 27^\circ = 90^\circ \)
   - **Answer:** Complementary.

2. \( m \angle 1 = 112^\circ \) and \( m \angle 2 = 68^\circ \)
   - Supplementary angles sum to \( 180^\circ \).
   - \( 112^\circ + 68^\circ = 180^\circ \)
   - **Answer:** Supplementary.

3. \( m \angle 1 = 24^\circ \) and \( m \angle 2 = 156^\circ \)
   - \( 24^\circ + 156^\circ = 180^\circ \)
   - **Answer:** Supplementary.

4. \( m \angle 1 = 72^\circ \) and \( m \angle 2 = 8^\circ \)
   - \( 72^\circ + 8^\circ = 80^\circ \), which is neither 90 nor 180.
   - **Answer:** Neither.

### Part 2: Determine if \( \angle 1 \) and \( \angle 2 \) are adjacent (based on diagrams).
1. **Yes**, the two angles share a common vertex and a common side.
2. **Yes**, they share a common vertex and a side.
3. **No**, the angles are not adjacent as they don’t share a vertex.
4. **Yes**, they share a common vertex and side.

### Part 3: Find the measure of \( \angle 2 \) if angles are complementary.
1. \( m \angle 1 = 23^\circ \)
   - \( m \angle 2 = 90^\circ - 23^\circ = 67^\circ \)
   - **Answer:** \( 67^\circ \).

2. \( m \angle 1 = 18^\circ \)
   - \( m \angle 2 = 90^\circ - 18^\circ = 72^\circ \)
   - **Answer:** \( 72^\circ \).

### Part 4: Find the measure of \( \angle 2 \) if angles are supplementary.
1. \( m \angle 1 = 35^\circ \)
   - \( m \angle 2 = 180^\circ - 35^\circ = 145^\circ \)
   - **Answer:** \( 145^\circ \).

2. \( m \angle 1 = 123^\circ \)
   - \( m \angle 2 = 180^\circ - 123^\circ = 57^\circ \)
   - **Answer:** \( 57^\circ \).

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Would you like more details on any of these solutions?

Here are some related questions:
1. What happens if two angles are neither complementary nor supplementary?
2. Can two angles be both adjacent and complementary?
3. How would you solve if angles are complementary in a triangle?
4. Can adjacent angles be equal?
5. How are adjacent angles different from vertical angles?

**Tip:** Always check if the sum of the angles meets the conditions for being complementary or supplementary (90° or 180°).

Given the measurements of angles, determine if they are complementary, supplementary, or neither. Also, determine if angles are adjacent. Find the measure of one angle if complementary or supplementary.

Learn how to determine if angles are complementary, supplementary, or adjacent based on their measurements. Find the missing angle if two angles are complementary or supplementary with step-by-step solutions. Suitable for students in Grades 6-8.

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