Question

State which definition, postulate, or theorem justifies the statement about the diagram.

$m\angle 1+m\angle 2=m\angle BAC$

Short answer

The Angle Addition Postulate justifies the statement about the diagram.

Step-by-step solution

Step 1. Observe the given diagram.

The diagram constitutes of a triangle ABC.

Step 2. State the Angle Addition Postulate.

The postulate states that if two angles are placed side by side, then the value of the resulting angle is equal to the sum of the original angles.

Step 3. State the conclusion.

Considering the given diagram and the statement “$m\angle 1+m\angle 2=m\angle BAC$”.

Here $\angle 1$and $\angle 2$are two adjacent angles. So, the sum of these two angles is equal to $\angle BAC$.

Therefore, the statement about the diagram is justified by the Angle Addition Postulate.