Math Problem Statement
answer it
Solution
The problem involves two intersecting lines, and we are given:
To solve this, follow these steps:
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Vertical Angle Theorem: Angles 1 and 3 are vertical angles, so they are equal. This means:
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Linear Pair: Angles 1 and 2 form a linear pair, meaning their measures add up to 180°. Therefore:
Substituting the expressions for the angles:
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Simplify the equation:
Combine like terms:
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Solve for :
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Find the measure of : Since :
So, the measure of is .
If you need any clarification, feel free to ask! Here are some related questions:
- What is the value of ?
- Can you explain the Vertical Angle Theorem in detail?
- How does the Linear Pair Postulate work in this context?
- What if the given angles were supplementary instead of vertical?
- Can we use this method to solve other angle relationships?
Tip: Always look for angle relationships (vertical, linear pair, etc.) when dealing with intersecting lines!
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Angle Relationships
Formulas
m∠1 + m∠2 = 180°
Theorems
Vertical Angle Theorem
Linear Pair Postulate
Suitable Grade Level
Grades 8-10
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