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Problem

\[A\]\[B\]\[C\]\[D\]\[E\]\[F\]\[G\]\[20^\circ\]\[50^\circ\]\[x^\circ\]

*NOTE: Angles not necessarily drawn to scale.*

\[x = \]  \[\Large{{}^\circ}\]

Do 10 problems

To solve the problem, let's first understand the diagram and the relationships between the angles. Although the diagram isn't provided, I'll guide you through the possible scenarios and how to solve them step-by-step. 

### Scenario 1: Given Angles in a Triangle

If the angles \(20^\circ\), \(50^\circ\), and \(x^\circ\) are inside a triangle:

1. **Sum of Angles in a Triangle:** The sum of all angles in a triangle is always \(180^\circ\).
2. **Equation Setup:** If \(20^\circ\), \(50^\circ\), and \(x^\circ\) are angles in a triangle, you would set up the equation as:
   \[
   20^\circ + 50^\circ + x^\circ = 180^\circ
   \]
3. **Solve for \(x^\circ\):**
   \[
   x^\circ = 180^\circ - 70^\circ = 110^\circ
   \]

### Scenario 2: Angles on a Straight Line

If the angles \(20^\circ\), \(50^\circ\), and \(x^\circ\) are on a straight line:

1. **Sum of Angles on a Straight Line:** The sum of angles on a straight line is \(180^\circ\).
2. **Equation Setup:** If \(20^\circ\) and \(50^\circ\) are adjacent angles to \(x^\circ\), then:
   \[
   20^\circ + 50^\circ + x^\circ = 180^\circ
   \]
3. **Solve for \(x^\circ\):**
   \[
   x^\circ = 180^\circ - 70^\circ = 110^\circ
   \]

### Scenario 3: Vertical Angles

If \(x^\circ\) is a vertical angle formed by \(20^\circ\) or \(50^\circ\):

1. **Vertical Angles are Equal:** Vertical angles are always equal.
2. **If \(x^\circ = 20^\circ\):**
   \[
   x^\circ = 20^\circ
   \]
3. **If \(x^\circ = 50^\circ\):**
   \[
   x^\circ = 50^\circ
   \]

### Conclusion:
Depending on the context:
- \(x = 110^\circ\) if angles are within a triangle or on a straight line.
- \(x\) could be \(20^\circ\) or \(50^\circ\) if they are vertical angles.

To solve additional similar problems, follow these steps based on the context:

### 5 Similar Problems to Try:
1. In a triangle, one angle is \(40^\circ\), and another is \(60^\circ\). What is the third angle?
2. Three angles on a straight line are \(30^\circ\), \(x^\circ\), and \(120^\circ\). Find \(x^\circ\).
3. Two angles in a triangle are \(90^\circ\) and \(45^\circ\). What is the remaining angle?
4. In a quadrilateral, three angles are \(80^\circ\), \(90^\circ\), and \(100^\circ\). Find the fourth angle.
5. Two vertical angles are formed by intersecting lines. If one angle is \(35^\circ\), what is the measure of the other?

**Tip:** Always pay attention to whether the problem involves a triangle, straight line, or intersecting lines to decide which angle rule to apply.

Learn how to solve a geometry problem involving angles in a triangle and on a straight line with angles 20°, 50°, and x°. Understand the relationships between these angles and solve for x° using triangle and straight line angle rules. Suitable for high school geometry students.

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