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)

Question

Responses

186° and 88°
186 degrees  and  88 degrees

125° and 55°
125 degrees  and  55 degrees

129° and 51°
129 degrees  and  51 degrees

121° and 59°

Answer 1

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

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

Now we can combine like terms:

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

This simplifies to:

\[ 3x - 3 = 180 \]

Next, we add 3 to both sides:

\[ 3x = 183 \]

Now, divide by 3:

\[ x = 61 \]

Now we can find the measures of the two angles:

1. The first angle: \[ 2x + 3 = 2(61) + 3 = 122 + 3 = 125° \]

2. 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°.

The correct response is:

125° and 55°.