Find the angle marked x in each geometric figure.

To solve for the angle marked \( x \) in each question, we will use geometric properties such as the sum of angles in a triangle, the sum of angles on a straight line, and the properties of parallel lines. Let's go through each problem step by step.

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Problem 1:

[Diagram shows a quadrilateral with angles \( 80^\circ \), \( 60^\circ \), and \( 70^\circ \). The angle \( x \) is opposite the \( 70^\circ \) angle.]

#### Solution:
The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
80^\circ + 60^\circ + 70^\circ + x = 360^\circ
\]
\[
210^\circ + x = 360^\circ
\]
\[
x = 360^\circ - 210^\circ = 150^\circ
\]

Answer: \( x = 150^\circ \)

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Problem 2:

[Diagram shows a quadrilateral with angles \( 130^\circ \), \( 60^\circ \), and \( 110^\circ \). The angle \( x \) is opposite the \( 110^\circ \) angle.]

#### Solution:
Again, the sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
130^\circ + 60^\circ + 110^\circ + x = 360^\circ
\]
\[
300^\circ + x = 360^\circ
\]
\[
x = 360^\circ - 300^\circ = 60^\circ
\]

Answer: \( x = 60^\circ \)

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Problem 3:

[Diagram shows a triangle with angles \( 50^\circ \), \( 70^\circ \), and an exterior angle of \( 120^\circ \). The angle \( x \) is the third interior angle of the triangle.]

#### Solution:
The sum of the interior angles of a triangle is \( 180^\circ \). Therefore:
\[
50^\circ + 70^\circ + x = 180^\circ
\]
\[
120^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 120^\circ = 60^\circ
\]

Answer: \( x = 60^\circ \)

---

Problem 4:

[Diagram shows a triangle with angles \( 30^\circ \), \( 70^\circ \), and an exterior angle of \( 120^\circ \). The angle \( x \) is the third interior angle of the triangle.]

#### Solution:
The sum of the interior angles of a triangle is \( 180^\circ \). Therefore:
\[
30^\circ + 70^\circ + x = 180^\circ
\]
\[
100^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 100^\circ = 80^\circ
\]

Answer: \( x = 80^\circ \)

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Problem 5:

[Diagram shows a quadrilateral with angles \( 75^\circ \), \( 120^\circ \), and \( 75^\circ \). The angle \( x \) is the fourth interior angle.]

#### Solution:
The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
75^\circ + 120^\circ + 75^\circ + x = 360^\circ
\]
\[
270^\circ + x = 360^\circ
\]
\[
x = 360^\circ - 270^\circ = 90^\circ
\]

Answer: \( x = 90^\circ \)

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Problem 6:

[Diagram shows a quadrilateral with angles \( 25^\circ \), \( 45^\circ \), and \( 95^\circ \). The angle \( x \) is the fourth interior angle.]

#### Solution:
The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
25^\circ + 45^\circ + 95^\circ + x = 360^\circ
\]
\[
165^\circ + x = 360^\circ
\]
\[
x = 360^\circ - 165^\circ = 195^\circ
\]

Answer: \( x = 195^\circ \)

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Problem 7:

[Diagram shows a hexagon with angles \( 60^\circ \), \( 120^\circ \), \( 120^\circ \), \( 120^\circ \), and two unknown angles. The angle \( x \) is one of the unknown angles.]

#### Solution:
The sum of the interior angles of a hexagon is given by:
\[
(6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
\]
The known angles are \( 60^\circ \), \( 120^\circ \), \( 120^\circ \), and \( 120^\circ \). Let the two unknown angles be \( x \) and \( y \). Therefore:
\[
60^\circ + 120^\circ + 120^\circ + 120^\circ + x + y = 720^\circ
\]
\[
420^\circ + x + y = 720^\circ
\]
\[
x + y = 300^\circ
\]
Since the hexagon is symmetric and the problem asks for \( x \), and there is no indication that \( x \) and \( y \) are different, we assume \( x = y \). Therefore:
\[
x + x = 300^\circ
\]
\[
2x = 300^\circ
\]
\[
x = 150^\circ
\]

Answer: \( x = 150^\circ \)

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Final Answers:

\[
\boxed{150^\circ, 60^\circ, 60^\circ, 80^\circ, 90^\circ, 195^\circ, 150^\circ}
\]