2 (45-x) 开 (2x +30) 于 5

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### Geometry Example Problems

This section includes example problems related to angles and their measures in various diagrams.

#### Problem 2:

The first diagram depicts two intersecting lines forming angles at point O. Here are the details given in the diagram for Problem 2:

- The diagram shows a right angle at point O on the left side, indicating it is part of a larger geometric configuration.
- There is an angle labeled \( (45 - x)^\circ \) near the intersection of the two lines.
- Another angle is labeled \( (2x + 30)^\circ \) near the intersection with point O.
- A segment is marked with a length of 5 units.

*Example Problem*
**Find the value of \( x \).**

#### Problem 4:

The second diagram for Problem 4 shows more complex geometry:

- Various lines intersect; labeled points J and M are shown.
- Angles are annotated with algebraic expressions: \( (10y + 60)^\circ \) and \( (2x)^\circ \).

Additionally, provided information and instruction is:
- A line segment \( \overline{B} \) bisects \( \angle AOC \).
- It asks for the measure \( m \angle AOC \).

*Instructions for Solving:*
1. Identify the relationships between the angles.
2. Use algebra to express these relationships.
3. Solve for the variables \( x \) and \( y \) as required.
4. Use the found values of variables to calculate the specific angle measures.

### Tips:
- Remember the properties of vertical angles, supplementary angles, and the sum of angles around a point.
- Utilize algebraic manipulation to solve for the unknowns.
- Make sure to double-check your calculated angle measures to ensure they adhere to geometric rules.

For further study, attempt to apply these methods to similar problems and verify your solutions for accuracy.
Transcribed Image Text:### Geometry Example Problems This section includes example problems related to angles and their measures in various diagrams. #### Problem 2: The first diagram depicts two intersecting lines forming angles at point O. Here are the details given in the diagram for Problem 2: - The diagram shows a right angle at point O on the left side, indicating it is part of a larger geometric configuration. - There is an angle labeled \( (45 - x)^\circ \) near the intersection of the two lines. - Another angle is labeled \( (2x + 30)^\circ \) near the intersection with point O. - A segment is marked with a length of 5 units. *Example Problem* **Find the value of \( x \).** #### Problem 4: The second diagram for Problem 4 shows more complex geometry: - Various lines intersect; labeled points J and M are shown. - Angles are annotated with algebraic expressions: \( (10y + 60)^\circ \) and \( (2x)^\circ \). Additionally, provided information and instruction is: - A line segment \( \overline{B} \) bisects \( \angle AOC \). - It asks for the measure \( m \angle AOC \). *Instructions for Solving:* 1. Identify the relationships between the angles. 2. Use algebra to express these relationships. 3. Solve for the variables \( x \) and \( y \) as required. 4. Use the found values of variables to calculate the specific angle measures. ### Tips: - Remember the properties of vertical angles, supplementary angles, and the sum of angles around a point. - Utilize algebraic manipulation to solve for the unknowns. - Make sure to double-check your calculated angle measures to ensure they adhere to geometric rules. For further study, attempt to apply these methods to similar problems and verify your solutions for accuracy.
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