Math Problem Statement
angle 1 and angle 2 form a linear pair. if angle 1 = 5x+9 and angle 2 = 3x-11 find the measure of each angle
Solution
To solve for the measures of Angle 1 and Angle 2, we first need to understand that a linear pair of angles are adjacent angles that add up to .
Given:
- Angle 1 =
- Angle 2 =
Since they form a linear pair: Substitute the given expressions:
Now, combine like terms:
Next, add 2 to both sides:
Now, divide both sides by 8:
Now that we have the value of , we can find the measures of the angles.
Angle 1:
Angle 2:
Thus, the measures of the angles are:
- Angle 1:
- Angle 2:
Would you like more details or have any questions?
Here are 5 related questions to deepen your understanding:
- What are supplementary angles, and how do they relate to a linear pair?
- How would the problem change if Angle 1 was equal to instead?
- Can two acute angles form a linear pair? Why or why not?
- How do linear pairs relate to the properties of parallel lines and a transversal?
- If the sum of the angles were instead, what would that imply?
Tip: Remember, the sum of angles in a linear pair is always , no matter the individual values of the angles.
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Math Problem Analysis
Mathematical Concepts
Angles
Linear pairs
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9