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Question

Difficulty: EasyLines and Angles

A metal worker is joining two pieces of steel such that the two adjacent angles formed make a straight line. The measure of the first angle is (2x+10)∘(2x + 10)^\circ and the measure of the second angle is (3x)∘(3x)^\circ. What is the measure of the first angle?

  1. 78∘78^\circAnswer
  2. B
    42∘42^\circ
  3. C
    58∘58^\circ
  4. D
    34∘34^\circ

Answer

The measure of the first angle is 78∘78^\circ.
Angles that form a straight line are supplementary and add up to 180 degrees. Setting up the equation (2x + 10) + 3x = 180 yields 5x + 10 = 180. Solving for x gives x = 34. Substituting this value into the expression for the first angle gives 2(34) + 10 = 78 degrees.

Step-by-Step Solution

1
Set up an equation based on the properties of a straight line.
(2x+10)+3x=180(2x + 10) + 3x = 180
Adjacent angles that form a straight line are supplementary, meaning their sum is exactly 180 degrees.
2
Combine like terms.
5x+10=1805x + 10 = 180
Adding the variable terms (2x and 3x) together simplifies the equation.
3
Solve for x.
x=34x = 34
Subtract 10 from both sides to get 5x = 170, then divide by 5 to isolate x.
4
Substitute the value of x back into the expression for the first angle.
2(34)+10=68+10=782(34) + 10 = 68 + 10 = 78
The question asks for the measure of the first angle, not just the value of x.

Key Concept

Supplementary Angles and Linear Equations
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Topics

Lines and Angles

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