Question

Solve Equations with Adjacent Angles Quick Check
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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

128°

120°

16°

52°

Answer 1

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Answer 2

To find the measure of the second angle, start by recognizing that adjacent angles on a straight line add up to 180°.

Given:
- First angle = \( (5x - 28)° \)
- Second angle = \( (8x)° \)

According to the straight angle theorem:
\[
(5x - 28) + (8x) = 180
\]

Combine like terms:
\[
13x - 28 = 180
\]

Now, add 28 to both sides:
\[
13x = 208
\]

Next, divide by 13:
\[
x = 16
\]

Now substitute \( x \) back into the expression for the second angle:
\[
8x = 8(16) = 128°
\]

Therefore, the measure of the second angle is:
\[
\boxed{128°}
\]