Given: δabc prove: m∠zab = m∠acb + m∠cba 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 Pairs; triangle angle sum property; equality and subtraction property.

The first statement says that  m∠ZAB + m∠CAB = 180°. These two angles are formed as linear pairs and from the Linear Pair postulate we know that if two angles form a linear pair, then the sum of their measures is 180°(1)

And 2nd statement stats m∠CAB + m∠ACB + m∠CBA = 180° which are angles inside the triangle. And from Angle sum property we know that the sum of the measures of the angles of a triangle is 180°.    (2)

From equation (1) and (2) we can equate m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.

Now, using subtraction property we will subtract m∠CAB from both the sides and hence, we get m∠ZAB = m∠ACB + m∠CBA which is our desire result.