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

121°
and 59°
121 degrees and 59 degrees

129°
and 51°

Answer 1

To determine the measures of the two angles that form a straight line (180°), we start by setting up an equation based on the information given. The angles are (2x + 3)° and (x - 6)°.

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

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

Now, we'll combine like terms:

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

Next, we add 3 to both sides:

\[
3x = 183
\]

Now, we divide by 3:

\[
x = 61
\]

Now we will substitute \( x = 61 \) back into the expressions for the angles to find their measures:

1. First angle:

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

2. Second angle:

\[
x - 6 = 61 - 6 = 55°
\]

Thus, the measures of the two angles that make up the straight line are:

- 125°
- 55°

The correct response is:

**125° and 55°**