Question

Write something you can conclude from the given information.

Given: $m\angle 1=m\angle 4$; $m\angle 2=m\angle 3$

Short answer

The obtained conclusion is$m\angle CBF=m\angle BCG$.

Step-by-step solution

Step 1. Write the actual angle of the numbered angles

Write the provided numbered angles in the alphabet.

$m\angle 1=\angle FBE$;

$m\angle 2=\angle EBC$;

$m\angle 3=\angle BCF$;

$m\angle 4=\angle FCG$

Step 2. Determine the angles that consist of the provided angles.

The $\angle CBF$is the addition of the angles $\angle EBF$and $\angle FBE$along with this$\angle BCG$ consists of angles$\angle BCF$ and $\angle FCG$. By using this information make two equations.

$\angle CBF=\angle EBC+\angle FBE$

$\angle BCG=\angle BCF+\angle FCG$

Step 3. Make the conclusion.

According to the obtained equations and the given equations, the addition of $m\angle 1$and $m\angle 2$is the same as the addition of $m\angle 3$and $m\angle 4$. So write an equation by using this information but write the angles in the alphabet,

$m\angle CBF=m\angle BCG$