Question

given : △abc
prove : m∠zab = m∠acb + m∠cba
we start with triangle abc and note 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

Explanation:

Step1: Linear Pair Postulate

By the Linear Pair Postulate, \(m\angle ZAB + m\angle CAB=180^{\circ}\)

Step2: Triangle Angle - Sum Theorem

In \(\triangle ABC\), by the Triangle Angle - Sum Theorem, \(m\angle CAB + m\angle ACB + m\angle CBA = 180^{\circ}\)

Step3: Subtraction Property of Equality

Since \(m\angle ZAB + m\angle CAB=m\angle CAB + m\angle ACB + m\angle CBA\), using the Subtraction Property of Equality (subtract \(m\angle CAB\) from both sides)

Answer:

\(m\angle ZAB=m\angle ACB + m\angle CBA\)