To solve for the measures of the two angles, we start by setting up the equation based on the information provided:
The two angles measure \((x - 5)^\circ\) and \((3x)^\circ\), and they are adjacent to each other, forming a resulting angle of \(107^\circ\).
Thus, we can write the equation:
\[ (x - 5) + (3x) = 107 \]
Now, simplify and solve for \(x\):
\[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \] \[ 4x = 107 + 5 \] \[ 4x = 112 \] \[ x = \frac{112}{4} \] \[ x = 28 \]
Now, we can find each angle:
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The first angle: \[ x - 5 = 28 - 5 = 23^\circ \]
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The second angle: \[ 3x = 3 \times 28 = 84^\circ \]
Now, rounding each angle to the nearest whole number:
First angle = \(23^\circ\)
Second angle = \(84^\circ\)
Thus, the measures of the two angles are:
23° and 84°
Therefore, the correct response is:
23° and 84°
1 answer