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The image contains a problem involving two geometric shapes with angles labeled, asking to find the missing values.

Let's break it down:

The task asks to "Find the values of *x* in the given figures. Show your solution completely." Both figures represent quadrilaterals with different sets of angles, where one or more angles are unknown and labeled as *x*.

1. **First figure:**
   - It is a quadrilateral.
   - Angles: 85°, 105°, 65°, and *x*.
   - The sum of all angles in a quadrilateral is always 360°.

   The equation becomes:
   \[
   85^\circ + 105^\circ + 65^\circ + x = 360^\circ
   \]
   Solving for *x*:
   \[
   x = 360^\circ - (85^\circ + 105^\circ + 65^\circ)
   \]

2. **Second figure:**
   - It is also a quadrilateral.
   - Angles: 85°, 70°, 150°, and *x*.
   - Similarly, the sum of all angles in this quadrilateral is 360°.

   The equation becomes:
   \[
   85^\circ + 70^\circ + 150^\circ + x = 360^\circ
   \]
   Solving for *x*:
   \[
   x = 360^\circ - (85^\circ + 70^\circ + 150^\circ)
   \]

Now, let me calculate the values for *x* in both cases.The missing angle values for the quadrilaterals are:

1. In the first figure, \( x = 105^\circ \).
2. In the second figure, \( x = 55^\circ \).

Would you like further details on the steps or have any other questions? Here are five related questions to consider:

1. How do you calculate the sum of interior angles in a polygon?
2. What is the general formula for the sum of interior angles of a polygon with *n* sides?
3. Why is the sum of the angles in a quadrilateral always 360°?
4. Can you find the missing angle in a triangle if two angles are known?
5. How can you apply these methods to irregular polygons?

**Tip:** Always remember that for any *n*-sided polygon, the sum of the interior angles is given by the formula: \( 180^\circ \times (n - 2) \).

Find the values of x in the given quadrilateral figures. Show your solution completely.

Learn how to find the missing angles in quadrilaterals using the sum of interior angles theorem. This problem involves calculating unknown angles labeled as x in two different figures, applying the formula that the sum of angles in a quadrilateral is always 360°. Suitable for Grades 6-8.

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