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 180180^\circ.

Given:

  • Angle 1 = 5x+95x + 9
  • Angle 2 = 3x113x - 11

Since they form a linear pair: Angle 1+Angle 2=180\text{Angle 1} + \text{Angle 2} = 180^\circ Substitute the given expressions: (5x+9)+(3x11)=180(5x + 9) + (3x - 11) = 180

Now, combine like terms: 5x+3x+911=1805x + 3x + 9 - 11 = 180 8x2=1808x - 2 = 180

Next, add 2 to both sides: 8x=1828x = 182

Now, divide both sides by 8: x=1828=22.75x = \frac{182}{8} = 22.75

Now that we have the value of xx, we can find the measures of the angles.

Angle 1: 5x+9=5(22.75)+9=113.75+9=122.755x + 9 = 5(22.75) + 9 = 113.75 + 9 = 122.75^\circ

Angle 2: 3x11=3(22.75)11=68.2511=57.253x - 11 = 3(22.75) - 11 = 68.25 - 11 = 57.25^\circ

Thus, the measures of the angles are:

  • Angle 1: 122.75122.75^\circ
  • Angle 2: 57.2557.25^\circ

Would you like more details or have any questions?


Here are 5 related questions to deepen your understanding:

  1. What are supplementary angles, and how do they relate to a linear pair?
  2. How would the problem change if Angle 1 was equal to 7x+27x + 2 instead?
  3. Can two acute angles form a linear pair? Why or why not?
  4. How do linear pairs relate to the properties of parallel lines and a transversal?
  5. If the sum of the angles were 200200^\circ instead, what would that imply?

Tip: Remember, the sum of angles in a linear pair is always 180180^\circ, 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