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Given the following information about the parallelogram, find the missing angles. Type the NUMBER only!                                                                                                                                     
 m∠1= 


m∠2= 


m∠3=


m∠4= 

°

We are given a parallelogram \( ABCD \), and several angles inside the figure. Let's analyze the angles and determine the missing ones.

### Given:
- \( m \angle ADC = 115^\circ \)
- \( m \angle ABC = 93^\circ \)
- \( m \angle DAB = 30^\circ \)
- \( m \angle AEB = 52^\circ \) (diagonal angles at the intersection)
- The numbers 1, 2, 3, 4 refer to angles that need to be found.

### Angle Analysis:
1. **Angle 1**:
   - \( \angle DAB = 30^\circ \) and \( \angle 1 \) are supplementary (since \( \angle DAB + \angle 1 = 180^\circ \) for any two angles along the same line).
   \[
   m \angle 1 = 180^\circ - 30^\circ = 150^\circ
   \]

2. **Angle 2**:
   - \( \angle AEB = \angle 2 \) because the diagonals of a parallelogram bisect each other and create equal angles.
   \[
   m \angle 2 = 52^\circ
   \]

3. **Angle 3**:
   - This angle is complementary to \( \angle ABC \) at vertex \( C \). Since \( m \angle ABC = 93^\circ \), and the total around a point is \( 180^\circ \):
   \[
   m \angle 3 = 180^\circ - 93^\circ = 87^\circ
   \]

4. **Angle 4**:
   - This is the angle opposite \( \angle 2 \) in the same way the diagonals bisect each other.
   \[
   m \angle 4 = 52^\circ
   \]

### Final Answers:
- \( m \angle 1 = 150^\circ \)
- \( m \angle 2 = 52^\circ \)
- \( m \angle 3 = 87^\circ \)
- \( m \angle 4 = 52^\circ \)

Would you like further clarification or details? Here are five related questions for deeper understanding:

1. How do you find the total sum of angles in any quadrilateral?
2. What is the property of diagonals in a parallelogram?
3. How can you confirm that opposite angles in a parallelogram are equal?
4. What are supplementary angles, and how are they useful in solving this problem?
5. How can the bisecting property of diagonals help in other geometric shapes?

**Tip**: In a parallelogram, opposite angles are always equal, and adjacent angles are supplementary.

Given the following information about the parallelogram, find the missing angles. Type the NUMBER only! m∠1= m∠2= m∠3= m∠4= °

Learn how to find the missing angles in a parallelogram based on given angle measures. This solution involves properties of supplementary angles, opposite angles, and diagonals bisecting each other. Suitable for students in Grades 8-10.

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