Answer:
Option C is correct.
\(14^{\circ}48'\) is the angle supplementary to the angle measuring \(165^{\circ}12'\)
Step-by-step explanation:
To find the angle supplementary to the angle measuring \(165^{\circ}12'\)
Let A be the angle supplementary to the angle measuring \(165^{\circ}12'\).
Supplementary Angles states that the two Angles are Supplementary when they add up to 180 degrees.
Use the conversion:
1 degree = 60 minute.
Then, we have the given angle \(165^{\circ}12'\) = \(165\frac{12}{60} =165\frac{1}{5} =165.2^{\circ}\)
Now, by definition of supplementary angle;
\(\angle A + 165.2^{\circ}= 180^{\circ}\)
Subtract 165.2 on both sides we get;
\(\angle A= 180^{\circ} - 165.2^{\circ} =14.8^{\circ} =14^{\circ}48'\)
Therefore, the angle supplementary to the angle measuring \(165^{\circ}12'\) is, \(14^{\circ}48'\)
