Q16 - Geometry

Question

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

Step-by-Step Solution

Answer

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

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