Question

What is the angle supplementary to the angle measuring 165°12′?

A. 75°12′
B. 180′
C. 14°48′
D. 60′

Answer 1

Two angles are supplementary if their sum is 180 degrees. One degree is made up of 60 minutes. So the angle supplementary to an angle measuring 165d12m is 180d - 165d12m, which gives us 14d48m. So the answer is C.

Answer 2

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, $14^{\circ}48'$