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

125°
and 55°
125 degrees and 55 degrees

186°
and 88°

Answer 1

To find the measures of the two angles that form a straight line (180°), you can set up the following equation based on the given angle measures:

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

Now, simplify the left side:

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

Next, add 3 to both sides:

\[ 3x = 183 \]

Now, divide by 3:

\[ x = 61 \]

Now, substitute \(x\) back into the angle expressions to 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: \[ x - 6 = 61 - 6 = 55° \]

Thus, the measures of the two angles are 125° and 55°.

The correct response is: 125° and 55°.