LA and ZB are supplementary. If the mZB is 49°, what is the m/A? What type of reasoning do you use, inductive or deductive, when solving this problem? Explain.

Given: $\angle A$ and $\angle B$ are supplementary and $m\angle B=49°$.

To find: $m\angle A$.

Solution:

We know that two angles are called supplementary if their sum is equal to $180°$.

We have given that $\angle A$ and $\angle B$ are supplementary.

Therefore,

$\begin{array}{rcl}m\angle A+m\angle B& =& 180°\\ m\angle A+49°& =& 180° \left[\text{Given} m\angle B=49°\right]\\ m\angle A& =& 180°-49°\\ m\angle A& =& 131°\end{array}$

Therefore, $m\angle A=131°$.