Question

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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Answer 1

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°.**