Question

Write the name or statement of the definition, postulate, or theorem that justifies the statement about the diagram.

If$\angle ADF$ and ∠4 are supplements, then $m\angle ADF+m\angle 4=180$.

Short answer

The statement of the definition which justifies the statement about the given diagram is the definition of the supplementary angles which states that the supplementary angles are the angles whose sum is 180° and the angles are said to be supplement of each other.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Definition of supplementary angles.

The supplementary angles are the angles whose sum is 180° and the angles are said to be supplement of each other.

Step 3. Write the statement of the definition that justifies the statement about the given diagram.

Given that∠ADFand∠4are supplements.

That implies the angles ∠ADF and∠4are supplementary angles, therefore the sum of the angles∠ADF and∠4is180°.

That implies,$m\angle ADF+m\angle 4=180°$

Therefore, the statement of the definition that justifies the statement about the given diagram is the definition of the supplementary angles which states that the supplementary angles are the angles whose sum is 180° and the angles are said to be supplement of each other.