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

128°
128 degrees

16°
16 degrees

52°
52 degrees

120°

Answer 1

Since the two angles are adjacent and lie on a straight line, their measures add up to 180°. We can set up the equation based on the angle measures provided:

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

Combining like terms gives:

\[
5x - 28 + 8x = 180
\]
\[
13x - 28 = 180
\]

Now, add 28 to both sides:

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

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

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

Now, we can use the value of \(x\) to find the measure of the second angle:

\[
8x = 8(16) = 128°
\]

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

**The answer is: 128°**