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?

Question

128

120

16

52

Answer 1

Since the two angles are adjacent and form a straight line, they are supplementary. This means their measures add up to 180 degrees.

Given:

1. First angle = \( 5x - 28 \)
2. Second angle = \( 8x \)

We can set up the equation: \[ (5x - 28) + 8x = 180 \]

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

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

Next, divide by 13: \[ x = \frac{208}{13} = 16 \]

Now, we can find the measure of the second angle: \[ 8x = 8(16) = 128 \]

Thus, the measure of the second angle is 128 degrees.