Question

What can you conclude from the information given?

Given: $\overrightarrow{AB}$bisects $\angle DAC$;

$\overrightarrow{CB}$bisects $\angle ECA$;

$m\angle 2=45$;

$m\angle 3=45$;

Short answer

The conclusion is $\overrightarrow{DA}\perp \overleftrightarrow{AC}$and $\overrightarrow{EC}\perp \overleftrightarrow{AC}$.

Step-by-step solution

Step 1. Definition of angle bisection.

An becomes a mixture of two angles having the same measurement when a line travels through it.

Step 2. Definition of perpendicular lines.

The definition of perpendicular lines states that the relation between two lines is perpendicular when the measurement of angles formed by those lines is equal to 90°.

Step 3. Observe the diagram and determine the value of ∠DAC

The ∠Step 4- Determine the value ofand represents itself as a right angle so its value will be equal to 90°.

Step 4. Determine the value of ∠1 and ∠2

The ∠DAC comprises angles ∠1 and ∠2 which are formed due to the line AB so according to the definition of angle bisection these angles are having the same measurement.

$\angle 1=\angle 2=45°$

Step 5. Make the conclusion.

As the ∠DAC comprises the angles ∠1 and ∠2 so the measurement of these angles will be equal to 90° if they are added together. This indicates that$\overrightarrow{DA}\perp \overleftrightarrow{AC}$ and $\overrightarrow{EC}\perp \overleftrightarrow{AC}$.