Math Problem Statement
Find the value of the varibles
Solution
The image shows two intersecting lines that form angles labeled , , and . These angles are connected by properties of vertical and adjacent angles.
Step 1: Identify relationships between the angles
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The angles and are vertical angles, so they are equal:
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The angles and are on a straight line, which means they are supplementary (their sum is 180°):
Step 2: Solve for
Step 3: Solve for
Since , we also have:
Final Answer:
Would you like further explanation on any step or more details?
Here are some related questions for deeper understanding:
- What are supplementary angles, and how do they apply here?
- Why are vertical angles equal?
- Can you explain the difference between supplementary and complementary angles?
- What is the significance of intersecting lines in geometry?
- How would this problem change if one of the angles were missing?
Tip: Always remember, vertical angles formed by intersecting lines are congruent!
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles
Vertical Angles
Supplementary Angles
Formulas
Vertical angles are congruent (equal)
Supplementary angles add up to 180 degrees
Theorems
Vertical Angles Theorem
Supplementary Angles Theorem
Suitable Grade Level
Grades 6-8
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