Question

Two Supplementary Angles Differ By $34°$. Find The Angles

Answer 1

Let the smaller angle be $x°$

Since the two angles differ by $34°$, the bigger angle$=x+34°$

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

Now, according to question,

$\begin{array}{rcl}x+(x+34)& =& 180°\\ 2x+34& =& 180°\\ 2x& =& 180-34\\ 2x& =& 146°\\ x& =& \frac{146°}{2}\\ x& =& 73°\end{array}$

The smaller angle $x=73°$

The bigger angle $=x+34=73+34=107°$

Hence, the supplementary angles are $73°and107°$.