Question

Find the complement of the following angles: $78°2\text{'}59"$

Answer 1

Let the required angle be $y$.

$\begin{array}{rcl}\therefore y+78°2\text{'}59\text{'}\text{'}& =& 90°\\ y& =& 90°-78°2\text{'}59\text{'}\text{'}\\ y& =& 89°59\text{'}60\text{'}\text{'}-78°2\text{'}59\text{'}\text{'}(As90°=89°59\text{'}60\text{'})\text{'}\\ y& =& 11°57\text{'}1\text{'}\text{'}\end{array}$

Hence, the complement of $78°2\text{'}59"$ is $11°57\text{'}1\text{'}\text{'}$.