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Difficulty: EasyLines and Angles

Two straight support beams on a bridge intersect at a single point. One of the angles formed by their intersection measures 74∘74^\circ. An adjacent angle along the straight line of one of the beams has a measure of (2x+16)∘(2x + 16)^\circ. What is the value of xx?

  1. A
    29
  2. 45Answer
  3. C
    61
  4. D
    90

Answer

45
Since the two angles form a linear pair along a straight support beam, their measures must sum to 180∘180^\circ. We can write the equation as 74+(2x+16)=18074 + (2x + 16) = 180. Combining like terms gives 2x+90=1802x + 90 = 180. Subtracting 9090 from both sides yields 2x=902x = 90. Finally, dividing by 22 gives x=45x = 45.

Step-by-Step Solution

1
Set up the equation using the property of supplementary angles.
74+(2x+16)=18074 + (2x + 16) = 180
Adjacent angles on a straight line form a linear pair, which means they are supplementary and sum to 180∘180^\circ.
2
Combine the constant terms on the left side of the equation.
2x+90=1802x + 90 = 180
Adding 7474 and 1616 simplifies the constant terms to 9090.
3
Isolate the variable term by subtracting 90 from both sides of the equation.
2x=902x = 90
Subtracting 9090 from 180180 leaves 9090 on the right side.
4
Solve for x by dividing both sides of the equation by 2.
x=45x = 45
Dividing 2x2x and 9090 by 22 isolates the variable xx.

Key Concept

Adjacent angles on a straight line are supplementary and add up to 180 degrees.
Estimated Time:45s
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Topics

Lines and Angles

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