Question

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

A. 75°12′
B. 180′
C. 14°48′
D. 60′

Answer 1

Option C is correct.

`14^(\circ)48'` is the angle supplementary to the angle measuring
`165^(\circ)12'`

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(12)/(60) =165(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'`

Answer 2

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.