Question

The measure of an angle is $102°24\text{'}35"$. Find the measure of its supplement .

Answer 1

Two angles are called supplementary when their measures add up to$180°.$

Now supplement of $102°24\text{'}35"$

$$\begin{gathered} =180°-102°24\text{'}35" \\ =179°+60\text{'}-\left(102°+24\text{'}+35"\right)\left[1°=60\text{'}\right] \\ =179°+59\text{'}+60\text{'}\text{'}-102°-24\text{'}-35"\left[1\text{'}=60\text{'}\text{'}\right] \\ =77°35\text{'}25\text{'}\text{'} \end{gathered}$$

Hence, supplement is $77°35\text{'}25\text{'}\text{'}$