Calculate the exterior angles of a quadrilateral if its three interior angles are 38°, 158°, 44°

In any quadrilateral, the sum of the interior angles is always \(360^\circ\). To find the exterior angle corresponding to each interior angle, remember that each pair of an interior and exterior angle is supplementary, summing up to \(180^\circ\).

Given three interior angles of a quadrilateral:
- \(38^\circ\)
- \(158^\circ\)
- \(44^\circ\)

1. **Find the fourth interior angle:**

   \[
   \text{Sum of interior angles} = 360^\circ
   \]
   \[
   38^\circ + 158^\circ + 44^\circ + x = 360^\circ
   \]
   \[
   x = 360^\circ - (38^\circ + 158^\circ + 44^\circ)
   \]
   \[
   x = 360^\circ - 240^\circ = 120^\circ
   \]

   So, the fourth interior angle is \(120^\circ\).

2. **Calculate the exterior angles:**

   Each exterior angle is found by subtracting the interior angle from \(180^\circ\).

   - For \(38^\circ\): \(180^\circ - 38^\circ = 142^\circ\)
   - For \(158^\circ\): \(180^\circ - 158^\circ = 22^\circ\)
   - For \(44^\circ\): \(180^\circ - 44^\circ = 136^\circ\)
   - For \(120^\circ\): \(180^\circ - 120^\circ = 60^\circ\)

   Therefore, the exterior angles are:
   \[
   142^\circ, 22^\circ, 136^\circ, \text{ and } 60^\circ
   \]

Would you like further details on any part of this solution? 

Here are some additional questions for practice:

1. How do you find the exterior angles if only two interior angles are known?
2. Why do the interior angles of a quadrilateral always sum to 360°?
3. Can a quadrilateral have all equal exterior angles?
4. What is the difference between interior and exterior angles in polygons?
5. How do exterior angles change as the number of polygon sides increases?

**Tip:** In any polygon, the exterior angles always add up to \(360^\circ\) regardless of the number of sides.

Calculate the exterior angles of a quadrilateral if its three interior angles are 38°, 158°, 44°.

Learn how to calculate the exterior angles of a quadrilateral when three of its interior angles are given. This problem involves basic geometry principles and exterior angle formulas. Suitable for students in Grades 6-8.

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