on a straight line two angles, one measures 2x+3 and the other is x-6, what are the measures of the two angles

Answer 1

On a straight line, the sum of the angles is \(180^\circ\). Given the two angles are \(2x + 3\) and \(x - 6\), we can set up the equation:

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

Now, simplify the equation:

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

Combine like terms:

\[ 3x - 3 = 180 \]

Now, add \(3\) to both sides:

\[ 3x = 183 \]

Next, divide by \(3\):

\[ x = 61 \]

Now we can find the measures of the two angles by substituting \(x\) back into the expressions for the angles.

1. For the angle \(2x + 3\):

\[ 2(61) + 3 = 122 + 3 = 125 \]

2. For the angle \(x - 6\):

\[ 61 - 6 = 55 \]

Thus, the measures of the two angles are:

• \(125^\circ\)
• \(55^\circ\)

These satisfy the condition that their sum is \(180^\circ\) (125 + 55 = 180).