Question

Two adjacent angles are on a straight line. One angle has a measure of (5x-28) degrees and the other angle has a measure of (8x) degrees. What is the measure of the second angle

Answer 1

Since the two angles are adjacent and on a straight line, their measures add up to 180 degrees. Therefore, we can set up the equation:

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

Now, combine the like terms:

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

This simplifies to:

\[
13x - 28 = 180
\]

Next, add 28 to both sides:

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

Now, divide both sides by 13 to solve for \(x\):

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

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

\[
8x = 8(16) = 128 \text{ degrees}
\]

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