To find the measures of the two adjacent angles formed by \( (x - 5)^\circ \) and \( (3x)^\circ \) where their sum equals \( 107^\circ \), we can set up the following equation:
\[ (x - 5) + (3x) = 107 \]
Now, simplify the equation:
\[ x - 5 + 3x = 107 \]
Combine like terms:
\[ 4x - 5 = 107 \]
Now, add 5 to both sides:
\[ 4x = 112 \]
Dividing both sides by 4 gives:
\[ x = 28 \]
Now we can find the measures of the two angles:
- \( (x - 5)^\circ \):
\[ x - 5 = 28 - 5 = 23^\circ \]
- \( (3x)^\circ \):
\[ 3x = 3 \times 28 = 84^\circ \]
Thus, the measures of the two angles are:
- \( 23^\circ \) and \( 84^\circ \)
To confirm that the resulting angle formed is obtuse and equal to \( 107^\circ \):
\[ 23^\circ + 84^\circ = 107^\circ \]
Both angle measures are correct.
So, the angle measures of the two unknown angles are \( 23^\circ \) and \( 84^\circ \).
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