https://file.aiquickdraw.com/mathbot/file/1725537755355s8goocbu.jpg

The image shows a polygon with various interior and exterior angles labeled, and the goal is to find the value of \( x^\circ \).

### Step-by-step explanation:

1. **Identify the interior angles:**
   The polygon has interior angles of 60°, 70°, 70°, and one unknown angle \( x \).

2. **Sum of interior angles of a polygon:**
   For a polygon with \( n \) sides, the sum of the interior angles is given by:
   \[
   S = (n - 2) \times 180^\circ
   \]
   This polygon has 5 sides (pentagon), so the sum of the interior angles is:
   \[
   S = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
   \]

3. **Set up the equation:**
   The sum of the given interior angles, including \( x \), should equal 540°:
   \[
   60^\circ + 70^\circ + 70^\circ + 70^\circ + x = 540^\circ
   \]

4. **Solve for \( x \):**
   First, sum up the known angles:
   \[
   60^\circ + 70^\circ + 70^\circ + 70^\circ = 270^\circ
   \]
   Now subtract this sum from 540°:
   \[
   x = 540^\circ - 270^\circ = 270^\circ
   \]

Thus, \( x = 270^\circ \).

Would you like more details or have any questions about this? Here are some related questions for further practice:

1. How do you calculate the sum of interior angles for a hexagon?
2. What is the difference between interior and exterior angles?
3. If a polygon has 8 sides, what is the sum of its interior angles?
4. How can exterior angles be used to find the sum of the interior angles?
5. What is the relationship between the sum of interior angles and the number of sides of a polygon?

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

Find the value of the unknown angle x in a polygon with various interior and exterior angles labeled.

Learn how to find the unknown angle in a pentagon using the sum of the interior angles. This geometry problem involves understanding polygons, calculating interior angles, and applying the polygon interior angle sum theorem. Suitable for students in Grades 7-9.

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