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Question

Difficulty: EasyLines and Angles

A surveyor is marking out a straight property boundary. Another reference line intersects this straight boundary, creating two adjacent angles. If the measure of the first angle is (5x)∘(5x)^\circ and the measure of the second angle is (4x+81)∘(4x + 81)^\circ, what is the value of xx?

  1. A
    2
  2. 11Answer
  3. C
    29
  4. D
    1

Answer

The value of x is 11.
Since the two adjacent angles form a straight line, they are supplementary and their measures must add up to 180 degrees. Setting up the equation 5x+4x+81=1805x + 4x + 81 = 180 allows us to combine like terms to get 9x+81=1809x + 81 = 180. Subtracting 81 from both sides gives 9x=999x = 99, and dividing by 9 results in x=11x = 11.

Step-by-Step Solution

1
Identify the geometric relationship between the two angles.
The angles form a linear pair, meaning their sum is 180∘180^\circ.
Adjacent angles that form a straight line are always supplementary.
2
Set up an algebraic equation.
5x+(4x+81)=1805x + (4x + 81) = 180
Substitute the given angle expressions into the supplementary angle relationship.
3
Combine the like terms on the left side of the equation.
9x+81=1809x + 81 = 180
Add the coefficients of the x terms (5x+4x=9x5x + 4x = 9x) while keeping the constant separate.
4
Isolate the variable term.
9x=999x = 99
Subtract 81 from both sides of the equation to balance it.
5
Solve for x.
x=11x = 11
Divide both sides by 9 to find the final value.

Key Concept

Supplementary Angles on a Straight Line
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Topics

Lines and Angles

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