Two adjacent angles are on a straight line. One angle has a measure of (5x−28)°

Question

and the other angle has a measure of (8x)°
. What is the measure of the second angle?(1 point)
Responses

120°
120 degrees

52°
52 degrees

16°
16 degrees

128°
128 degrees

Answer 1

To find the measure of the second angle, we start by using the fact that two adjacent angles on a straight line sum up to 180°.

Let the first angle be \( (5x - 28)° \) and the second angle be \( (8x)° \).

Setting up the equation:

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

Combining like terms:

\[ 13x - 28 = 180 \]

Now, add 28 to both sides:

\[ 13x = 208 \]

Next, divide by 13:

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

Now that we have the value of \( x \), we can substitute it back into the expression for the second angle:

\[ 8x = 8(16) = 128° \]

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