To find the measures of the two unknown angles, we will set up the equation based on the information given. The problem states that the obtuse angle is formed by two adjacent angles measuring \((x - 5)°\) and \((3x)°\), and together they form an angle of \(107°\). We can set up the following equation:
\[ (x - 5) + (3x) = 107 \]
Combining like terms:
\[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \]
Now, we'll add \(5\) to both sides:
\[ 4x = 112 \]
Next, we divide by \(4\):
\[ x = 28 \]
Now we can find the measures of the two angles:
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The first angle: \[ x - 5 = 28 - 5 = 23° \]
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The second angle: \[ 3x = 3(28) = 84° \]
Thus, the measures of the two unknown angles are:
- \(23°\)
- \(84°\)
Therefore, the angle measures of each of the two unknown angles are 23° and 84°.
The correct response is 23° and 84°.