Q15 - Geometry

Question

Complete. $m\angle 3+m\angle 4=m\angle ?$

Step-by-Step Solution

Answer

The answer is $m\angle 3+m\angle 4=\mathit{m}\mathbf{\angle }\mathit{A}$

Step 1. Observe the diagram.

From the given figure, it is observed that $\angle DAL=m\angle 3$ and $\angle DAE=m\angle 4$.

Step 2. Description of step.

Since, $\angle LAS=m\angle A$ such that $\angle LAS=\angle DAL+\angle DAE$.

Step 3. Calculate m∠3m+∠4=m∠?

In order to find $m\angle 3+m\angle 4$, substitute $m\angle 3$ for $\angle DAL$ and $m\angle 4$ for $\angle DAE$ into $\angle LAS=\angle DAL+\angle DAE$.

$\begin{array}{l}\angle LAS=\angle DAL+\angle DAE\\ =m\angle 3+m\angle 4\\ m\angle A=m\angle 3+m\angle 4\end{array}$

Therefore, $m\angle 3+m\angle 4=m\angle A$.