Question

Two complementary angles differ by $10$ degrees. Find the angles.

Answer 1

Finding the angles:

Let the first angle be $x$.

Then its complementary angle will be $90–x$

The difference of the complementary angles is $10$ degrees.

$\begin{array}{rcl}x–(90°–x)& =& 10°\\ x–90°+x& =& 10°\\ 2x& =& 10°+90°\\ 2x& =& 100°\\ x& =& 50°\end{array}$

Second angle$=90°–50°=40°$

Therefore, the two angles are $50°$ and $40°$ respectively.