Math Problem Statement
Solution
To solve this diagram, we need to determine the values of the numbered angles labeled 1 through 5. Here's the step-by-step analysis:
Step 1: Identify Relationships and Given Angles
- The diagram shows two intersecting lines with angles formed around them.
- Angles given in the triangles are 50°, 65°, 68°, and 140°.
- The numbered angles (1 to 5) are labeled, and we need to find their values.
Step 2: Use Triangle Angle Sum Property
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Triangle with 50° and 65°:
- The sum of the angles in any triangle is 180°.
- Let's find the third angle (angle 1): So, angle 1 = 65°.
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Triangle with 68°:
- The other angle needed is angle 5: So, angle 5 = 62°.
Step 3: Use Linear Pairs and Vertical Angles
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Angle 2:
- Since angle 1 is 65° and angles on a straight line sum to 180°,
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Angle 3 and angle 4:
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Both are vertical angles opposite 50° and 140°, respectively, and follow vertical angle rules, thus the values remain:
- Angle 3 = 50°
- Angle 4 = 140°
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Conclusion:
- Angle 1: 65°
- Angle 2: 115°
- Angle 3: 50°
- Angle 4: 140°
- Angle 5: 62°
Would you like further clarifications or additional information?
Related Questions:
- How do the linear pair relationships affect angle measurements?
- Why are the vertical angles always equal?
- How can you determine an unknown angle in a triangle?
- What role does symmetry play in these angle relationships?
- What are alternate angles, and how do they differ from vertical?
Tip:
Always look for straight lines or intersecting lines first to leverage basic geometric rules like vertical angles, linear pairs, and triangle sum rules.
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Math Problem Analysis
Mathematical Concepts
Geometry
Angle Relationships
Triangle Angle Sum Property
Formulas
Triangle angle sum: 180°
Linear pair: Angles on a straight line sum to 180°
Vertical angles: Opposite angles are equal
Theorems
Triangle Angle Sum Theorem
Vertical Angle Theorem
Linear Pair Postulate
Suitable Grade Level
Grades 7-10