Question

Two adjacent angles are on a straight line. One angle has a measure of (5x−28)°
and the other angle has a measure of (8x)°
. What is the measure of the second angle?(1 point)
Responses

16°
16 degrees

120°
120 degrees

52°
52 degrees

128°

Answer 1

Since the two angles are adjacent and on a straight line, they are supplementary, which means their measures add up to 180°.

We can set up the equation:

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

Now, combine like terms:

\[
13x - 28 = 180
\]

Next, add 28 to both sides:

\[
13x = 208
\]

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

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

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

\[
8x = 8(16) = 128°
\]

So, the measure of the second angle is \(128°\).

Thus, the correct answer is:

128°