We start with triangle abc and see that angle zab is an exterior angle created by the extension of side ac. angles zab and cab are a linear pair by definition. we know that m∠zab + m∠cab = 180° by the . we also know m∠cab + m∠acb + m∠cba = 180° because . using substitution, we have m∠zab + m∠cab = m∠cab + m∠acb + m∠cba. therefore, we conclude m∠zab = m∠acb + m∠cba using the .

Linear Pair postulate; triangle angle sum conjecture; subtraction property of equality.

Step-by-step explanation:

The Linear Pair postulate states that if two angles form a linear pair, then the sum of their measures is 180°.  This is the reason for the first statement.

The Triangle Angle Sum conjecture states that the sum of the measures of the angles of a triangle is 180°.  This is the reason for the second statement.

In order to isolate m∠ZAB, we must subtract m∠CAB from each side.  The subtraction property of equality is what allows us to do this.