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

128°
128 degrees

52°

Answer 1

Since the two angles are adjacent and along a straight line, their measures must add up to 180°.

We can set up the equation based on the measures of the angles:

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

Now, combine like terms:

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

Next, add 28 to both sides:

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

Now, divide by 13:

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

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

\[
8x = 8(16) = 128°
\]

Therefore, the measure of the second angle is **128°**.