Question

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

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

Short answer

The postulate that justifies the given statement is the Angle Addition Postulate.

Step-by-step solution

Step 1. Find the interior angles of ∠ABC.

Observe that both the angles ∠1 and ∠2 are interior of$\angle ABC$.

Step 2. Determine the theorem or postulate that can be used.

Postulate 4, the Angle Addition Postulate, states that if lies in the interior of $\angle AOC$, then$m\angle AOB+m\angle BOC=m\angle AOC$.

Step 3. Use the postulate.

So, the sum of the angles∠1and ∠2 is equal to $\angle ABC$by the angle addition postulate.

That is,$m\angle 1+m\angle 2=m\angle ABC$.