Math Problem Statement
Solution
To solve this problem, let's first break down the information provided:
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and are a linear pair. This means that they are adjacent angles formed by two intersecting lines, and their measures add up to .
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is four times larger than . Mathematically, this can be written as:
Let . Then, .
Since and form a linear pair, we have: Substituting the expressions for and into this equation:
Therefore, .
Now, to find :
Final Answer:
The measure of is .
Would you like further details or explanations on this solution?
Here are five related questions to explore:
- What is the measure of when and are linear pairs and is twice ?
- Can the measure of ever be greater than if and are linear pairs?
- How do the properties of supplementary angles relate to linear pairs?
- What would happen if was only three times ?
- How does the concept of vertical angles relate to linear pairs?
Tip: When dealing with linear pairs, remember that the sum of the angles will always be . This property is key to solving many geometric problems involving straight lines and adjacent angles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Linear Pairs
Supplementary Angles
Formulas
∠C + ∠D = 180°
∠C = 4 × ∠D
Theorems
Linear Pair Theorem
Supplementary Angles Theorem
Suitable Grade Level
Grades 8-10