To find the measures of the two angles, we first set up the equation based on the information provided. The two angles are \((x - 5)^\circ\) and \((3x)^\circ\), and their sum is equal to \(107^\circ\).
We can write the equation as:
\[ (x - 5) + (3x) = 107 \]
Combining like terms gives:
\[ 4x - 5 = 107 \]
Next, we add 5 to both sides:
\[ 4x = 112 \]
Now, we divide by 4:
\[ x = 28 \]
Now that we have the value of \(x\), we can find the measures of the two angles:
- First angle: \(x - 5 = 28 - 5 = 23^\circ\)
- Second angle: \(3x = 3(28) = 84^\circ\)
Thus, the measures of the angles are \(23^\circ\) and \(84^\circ\).
The answer is:
23° and 84°
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