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 40 degrees, 25 minutes, 16 seconds. What is the measure of ∠K?

Answer 1

Answer: The measure of angle J is 40 degrees, 25 minutes, and 16 seconds, which can be expressed in decimal form as 40 + 25/60 + 16/3600 = 40.42111... degrees.

Since ∠J and ∠K are complementary, their measures add up to 90 degrees.

So, the measure of ∠K can be found by subtracting the measure of ∠J from 90 degrees:

∠K = 90 - 40.42111... = 49.57888... degrees

So, the measure of ∠K is approximately 49 degrees, 34 minutes, and 44 seconds.

Explanation: