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

129°
and 51°
129 degrees and 51 degrees

121°
and 59°
121 degrees and 59 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°), we can set up the equation based on the angle measures provided. We know that:

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

Now simplify and solve for \( x \):

1. Combine like terms: \[ 2x + 3 + x - 6 = 180 \] Simplifies to: \[ 3x - 3 = 180 \]

2. Add 3 to both sides: \[ 3x = 183 \]

3. Divide by 3: \[ x = 61 \]

Now, substitute \( x \) back into the expressions for the 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 that make up the straight line are:

125° and 55°.

So the correct response is: 125° and 55°.