Solve Equations with Adjacent Angles Quick Check

Question

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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

52°
52 degrees

120°
120 degrees

128°
128 degrees

16°
16 degrees
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Answer 1

To find the measure of the second angle, we need to use the fact that the sum of two adjacent angles on a straight line is 180°.

Given:

• One angle is \((5x - 28)°\)
• The other angle is \((8x)°\)

We can set up the equation:

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

Now, simplify the equation:

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

Next, add 28 to both sides:

\[ 13x = 208 \]

Now, divide both sides by 13:

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

Now that we found \(x\), we can find the measure of the second angle:

Substituting \(x = 16\) into the second angle's expression:

\[ 8x = 8(16) = 128° \]

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