A 180°

Question

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

129°
and 51°
129 degrees and 51 degrees

186°
and 88°
186 degrees and 88 degrees

125°
and 55°

Answer 1

To determine the measures of the two angles that form a straight line (180°), we can set up an equation based on the information given:

The two angles are:

1. (2x + 3)°
2. (x - 6)°

Since they form a straight line, we can write the equation:

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

Now, simplify the equation:

\[ 2x + 3 + x - 6 = 180 \] \[ 3x - 3 = 180 \] \[ 3x = 180 + 3 \] \[ 3x = 183 \] \[ x = \frac{183}{3} = 61 \]

Now 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): \[ 61 - 6 = 55° \]

So, the measures of the two angles that make up the straight line are 125° and 55°.

Therefore, the correct response is:

125° and 55°.