Question

Write something you can conclude from the given information.

Given: $\angle 4$and $\angle 6$are complements.

Short answer

The required conclusion is$\overrightarrow{CG}\perp \overleftrightarrow{AD}$.

Step-by-step solution

Step 1. Definition of complementary angles.

Angles having the measurement of when they added are referred as the complementary angles.

Step 2. Write the addition of provided angles.

By using the definition make an equation that represents the addition of provided angles.

$\angle 4+\angle 6=90°$

Step 3. Definition of vertically opposite angles.

According to the definition of vertically opposite angles are referred as those angles which are formed when a line travels from two separate lines and the measurement of these angles is the same.

Step 4. Use the definition of vertically opposite angles.

The angles that are vertically opposite in the figure are $\angle 6$and $\angle 3$so make an equation by using the property of these angles.

$\angle 6=\angle 3$

Rewrite the equation$\angle 4+\angle 6=90°$ by substituting $\angle 3$at the place of $\angle 6$.

$\angle 3+\angle 6=90°$

Step 5. Make the conclusion.

The angles$\angle 3$ and$\angle 4$ are the part of$\angle BCG$ so the measurement of$\angle BCG$ will be 90°. Use the definition of perpendicular lines that is the relation between two lines is perpendicular when the measurement of angles formed by those lines is equal to 90°.

The angle$\angle BCG$ is formed by the lines$\overrightarrow{CG}$ and$\overleftrightarrow{AD}$ which means that the relation between these lines is perpendicular so make an equation for this and this will be the conclusion.

$\overrightarrow{CG}\perp \overleftrightarrow{AD}$