two adjacent angles on a straight line . one angle measures 5x-28 and the other measures 8x what is the measure of the second angle

Answer 1

Since the two angles are adjacent on a straight line, they are supplementary, meaning they add up to \(180^\circ\).

Given the two angles:

1. \( 5x - 28 \)
2. \( 8x \)

We can set up the equation:

\[ (5x - 28) + 8x = 180 \]

Now, combine like terms:

\[ 13x - 28 = 180 \]

Next, add \(28\) to both sides:

\[ 13x = 180 + 28 \] \[ 13x = 208 \]

Now, divide both sides by \(13\):

\[ x = \frac{208}{13} \] \[ x = 16 \]

Now, we can find the measure of the second angle, which is \(8x\):

\[ 8x = 8(16) = 128 \]

Thus, the measure of the second angle is \( \boxed{128} \).