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What is the answer of the interior and exterior 

The image you provided shows a polygon with the following labeled angles:

- Interior angles: 85°, 119°, 105°, and 109°.
- Exterior angles are not directly labeled but can be calculated using the formula \( \text{Exterior Angle} = 180^\circ - \text{Interior Angle} \).

### Interior Angles:
The sum of the given interior angles can be calculated directly:

\[
\text{Sum of Interior Angles} = 85^\circ + 119^\circ + 105^\circ + 109^\circ
\]

\[
\text{Sum of Interior Angles} = 418^\circ
\]

### Exterior Angles:
Each exterior angle can be found by subtracting the interior angle from 180°:

- \( \text{Exterior Angle 1} = 180^\circ - 85^\circ = 95^\circ \)
- \( \text{Exterior Angle 2} = 180^\circ - 119^\circ = 61^\circ \)
- \( \text{Exterior Angle 3} = 180^\circ - 105^\circ = 75^\circ \)
- \( \text{Exterior Angle 4} = 180^\circ - 109^\circ = 71^\circ \)

### Sum of Exterior Angles:
For any polygon, the sum of the exterior angles is always 360°.

#### Summary:
- **Sum of Interior Angles**: 418°
- **Individual Exterior Angles**: 95°, 61°, 75°, and 71°
- **Sum of Exterior Angles**: 360°

Would you like to go deeper into any specific part of this problem? Here are five related questions to consider:

1. How can you verify that the sum of the interior angles is correct for a quadrilateral?
2. What is the relationship between interior and exterior angles in polygons?
3. How would the problem change if this were a pentagon instead of a quadrilateral?
4. Can you determine if this shape is a regular polygon based on the angles provided?
5. What is the significance of the sum of exterior angles always being 360°?

**Tip:** Remember that the sum of interior angles in any polygon can be determined using the formula \( (n-2) \times 180^\circ \), where \( n \) is the number of sides.

What is the answer of the interior and exterior angles of the polygon shown in the image?

Discover how to calculate the interior and exterior angles of a quadrilateral. This problem involves key geometric concepts, such as the sum of interior angles, exterior angle calculation, and understanding the Sum of Exterior Angles Theorem. Suitable for students in Grades 6-8.

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