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

128°

120°

16°

52°

Answer 1

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: \[ \boxed{128°} \]

Answer 2

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