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

121°
and 59°
121 degrees and 59 degrees

186°
and 88°
186 degrees and 88 degrees

129°
and 51°
129 degrees and 51 degrees

125°
and 55°

Answer 1

To find the measures of the two angles that make up the straight line (180°), we can set up the equation based on the given expressions for the angles.

Let the two angles be:
- First angle: \( (2x + 3)° \)
- Second angle: \( (x - 6)° \)

Since they form a straight line, we can set up the following equation:

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

Now, combine the terms:

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

This simplifies to:

\[
3x - 3 = 180
\]

Next, add 3 to both sides:

\[
3x = 183
\]

Now, divide by 3:

\[
x = 61
\]

Now that we have the value of \( x \), we can find the measures of the two angles:

1. For the first angle:

\[
2x + 3 = 2(61) + 3 = 122 + 3 = 125°
\]

2. For the second angle:

\[
x - 6 = 61 - 6 = 55°
\]

Therefore, the measures of the two angles are \( 125° \) and \( 55° \).

The correct response is: **125° and 55°**.