Question

Two supplementary angles differ by $48°$. Find the angles.

Answer 1

Let the smaller angle be $x°$

Since the two angles differ by $48°$, the bigger angle$=x+48°$

Since the sum of the supplementary angles is $180°$

Now, according to question,

$\begin{array}{rcl}x+(x+48)& =& 180°\\ 2x+48& =& 180°\\ 2x& =& 180-48\\ 2x& =& 132°\\ x& =& \frac{132°}{2}\\ x& =& 66°\end{array}$

The smaller angle $x=66°$

The bigger angle $=x+48=66+48=114°$

Hence, the supplementary angles are $66°and114°$.