Math Problem Statement
Solution
To solve for the value of angle in the provided diagram, let's break this down step by step:
Analyzing the Given Information
- The diagram shows intersecting lines, creating vertical and supplementary angles.
- Given angles:
- One angle is .
- Adjacent to it, there is an angle of .
- The angle needs to be determined.
Using Geometrical Relationships
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Angles on a straight line: When two angles share a straight line, their sum is because they are supplementary angles.
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Vertical angles: Angles opposite each other at the intersection of two lines are equal.
Solving for :
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The angle adjacent to and forms a straight line. Therefore:
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Now, angle and also form a straight line. Hence:
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Solving for :
Final Answer:
The value of is .
Let me know if you'd like further clarification or additional details! Here are related questions you may find useful:
- How do supplementary and vertical angles relate to intersecting lines?
- What are alternate interior angles and how are they used in solving geometry problems?
- Can you explain the angle sum property of a triangle?
- How can you determine missing angles when two parallel lines are cut by a transversal?
- What is the difference between complementary and supplementary angles?
Tip: Always look for straight-line relationships or opposite (vertical) angles when solving for unknown angles in intersecting line diagrams.
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles formed by intersecting lines
Supplementary angles
Vertical angles
Formulas
Supplementary angles: a + b = 180°
Vertical angles are equal
Theorems
Supplementary Angles Theorem
Vertical Angles Theorem
Suitable Grade Level
Grades 8-10