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Let's go through the angles step-by-step to find the measures of each angle labeled \( m\angle1 \) to \( m\angle7 \).

### Step-by-Step Solution

1. **Identify given angles:**
   - \( m\angle6 = 144^\circ \)
   - \( m\angle4 = 95^\circ \)
   - \( m\angle7 = 38^\circ \)
   - There is also a right angle marked near \( m\angle1 \), indicating \( m\angle1 = 90^\circ \).

2. **Find \( m\angle2 \):**
   - \( m\angle2 \) and \( m\angle4 \) form a linear pair (they are supplementary because they are on a straight line).
   - So, \( m\angle2 = 180^\circ - 95^\circ = 85^\circ \).

3. **Find \( m\angle5 \):**
   - \( m\angle5 \) and \( m\angle6 \) form a linear pair.
   - Thus, \( m\angle5 = 180^\circ - 144^\circ = 36^\circ \).

4. **Find \( m\angle3 \):**
   - \( m\angle3 \) and \( m\angle2 \) are vertically opposite angles, so they are equal.
   - Therefore, \( m\angle3 = m\angle2 = 85^\circ \).

### Summary of Angle Measures

- \( m\angle1 = 90^\circ \)
- \( m\angle2 = 85^\circ \)
- \( m\angle3 = 85^\circ \)
- \( m\angle4 = 95^\circ \)
- \( m\angle5 = 36^\circ \)
- \( m\angle6 = 144^\circ \)
- \( m\angle7 = 38^\circ \)

Would you like further clarification on any of the steps?

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### Related Questions

1. What is the sum of all interior angles in a polygon?
2. How do you identify vertically opposite angles?
3. What is a linear pair of angles, and how do they help in solving angle problems?
4. What are supplementary angles?
5. How can you determine angle measures in complex geometric figures?

### Tip

In geometry, using properties of angles, such as linear pairs and vertical angles, can simplify complex diagrams significantly. Look for known relationships first to tackle challenging problems more easily.

Find the measures of angles m∠1 to m∠7 based on the given geometric figure with labeled angles and angles on straight lines.

Find the measures of angles m∠1 to m∠7 in a geometric figure using properties like supplementary angles and vertically opposite angles. Learn how to solve for unknown angles with given angle measures of 144°, 95°, and 38°.

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