To find the measures of the two angles, we set up the equation based on the given information:
The two angles are:
- \( (x - 5)^\circ \)
- \( (3x)^\circ \)
These two angles add up to create an obtuse angle of \( 107^\circ \): \[ (x - 5) + (3x) = 107 \]
Combining like terms gives: \[ 4x - 5 = 107 \]
Next, we add \( 5 \) to both sides: \[ 4x = 112 \]
Now, divide by \( 4 \): \[ x = 28 \]
Now we substitute \( x \) back into the expressions for the two angles:
- \( (x - 5) = (28 - 5) = 23^\circ \)
- \( (3x) = (3 \times 28) = 84^\circ \)
Thus, the measures of the two angles are:
- \( 23^\circ \)
- \( 84^\circ \)
So, the correct response is \( 23^\circ \) and \( 84^\circ \).