Question

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

Explanation:

Step1: Identify first blank reason

Linear pair angles sum to 180°, so reason is linear pair postulate.

Step2: Identify second blank reason

Triangle angles sum to 180°, so reason is triangle angle sum theorem.

Step3: Identify third blank reason

Subtract \(m\angle CAB\) from both sides, so reason is subtraction property of equality.

Answer:

1. Linear Pair Postulate
2. Triangle Angle Sum Theorem
3. Subtraction Property of Equality