Question

Complete. $m\angle ALS-m\angle 2=m\angle ?$

Short answer

The answer is$m\angle ALS-m\angle 2=\mathit{m}\mathbf{\angle }\mathbf{1}$

Step-by-step solution

Step 1. Observe the diagram.

From the given figure, it is observed that $\angle ALE=m\angle 2$and $\angle ELS=m\angle 1$.

Step 2. Description of step.

Clearly, $\angle ALS=\angle ALE+\angle ELS$.

Step 3. Calculate m∠ALS-m∠2=m∠?

In order to find $m\angle ALS-m\angle 2$, substitute$m\angle 2$for $\angle ALE$and $m\angle 1$ for $\angle ELS$into$\angle ALS=\angle ALE+\angle ELS$and then subtract $m\angle 2$from both sides of the equation.

$\begin{array}{l}\angle ALS=\angle ALE+\angle ELS\\ =m\angle 2+m\angle 1\\ \angle ALS-m\angle 2=m\angle 2+m\angle 1-m\angle 2\\ \angle ALS-m\angle 2=m\angle 1\end{array}$

Therefore, $m\angle ALS-m\angle 2=m\angle 1$.