Question

Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that ∠J and ∠K are complementary, and that the measure of ∠J is 41 degrees, 32 minutes, 33 seconds. What is the measure of ∠K?

The measure of ∠K is ___ degrees, ___ minutes, and ___ seconds.

Answer 1

The measure of ∠K is 49 degrees, 28 minutes, and 27 seconds.

Explanation:

The complementary angles is the sum of two angles which has total 90°.

Form the given information,

One degree is equal to 60 minutes and 1 minute is equal to 60 seconds.

If ∠J and ∠K are the complementary angles then their sum will be 90°.

we know that the ∠J is 41°32'33".

∴ 41°32'33"+∠K = 90°60'60".

∠K = 90°60'60" - 41°32'33".

∠K = 49°28'27".