Solve Equations with Adjacent Angles Quick Check

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Question
A 180°
angle (straight line) is formed by two adjacent angles. One angle has a measure of (2x+3)°
and the other has a measure of (x−6)°
. What are the measures of the two angles that make up the straight line?(1 point)
Responses

125°
and 55°
125 degrees and 55 degrees

186°
and 88°
186 degrees and 88 degrees

129°
and 51°
129 degrees and 51 degrees

121°
and 59°
121 degrees and 59 degrees
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1 answer

To find the measures of the two adjacent angles that add up to 180°, we can set up the equation based on the information given:

  1. The first angle is \( (2x + 3)° \).
  2. The second angle is \( (x - 6)° \).

Since they form a straight line, their sum should equal 180°:

\[ (2x + 3) + (x - 6) = 180 \]

Now, combine like terms:

\[ 2x + 3 + x - 6 = 180 \] \[ 3x - 3 = 180 \]

Next, add 3 to both sides:

\[ 3x = 183 \]

Now, divide by 3:

\[ x = 61 \]

Now we can find the measure of each angle by substituting \( x \) back into the expressions for each angle.

  1. The first angle: \[ 2x + 3 = 2(61) + 3 = 122 + 3 = 125° \]

  2. The second angle: \[ x - 6 = 61 - 6 = 55° \]

Thus, the two adjacent angles that form a straight line measure:

\(\boxed{125°}\) and \(\boxed{55°}\).

So the correct response is 125° and 55°.