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?

125 and 55

186 and 88

129 and 51

121 and 59

1 answer

To find the measures of the two adjacent angles formed by the straight line, we can set up the following equation based on the fact that the sum of the angles should equal \( 180 \) degrees:

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

Now, let's simplify and solve for \( x \):

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

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

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

Now we can find the measures of the two angles:

  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 \( 125 \) degrees and \( 55 \) degrees.

So the answer is:

125 and 55.