given: $ \triangle abc $
prove: $ m \angle zab = m \angle acb + m \angle 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 \angle zab + m \angle cab = 180 ^ { \circ } $ by the
we also know $ m \angle cab + m \angle acb + m \angle cba = 180 ^ { \circ } $
because
using substitution, we have $ m \angle zab + m \angle cab = $
$ m \angle cab + m \angle acb + m \angle cba $.
therefore, we conclude $ m \angle zab = m \angle acb + $
$ m \angle cba $ using the

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Accepted Answer

# Explanation:
## Step1: Linear Pair Postulate
Since $ \angle ZAB$ and $ \angle CAB$ are a linear pair, by the Linear Pair Postulate, $ m\angle ZAB + m\angle CAB=180^{\circ}$
## Step2: Triangle Angle - Sum Theorem
For $\triangle ABC$, by the Triangle Angle - Sum Theorem, $m\angle CAB + m\angle ACB + m\angle CBA = 180^{\circ}$
## Step3: Subtraction Property of Equality
We have $m\angle ZAB + m\angle CAB=m\angle CAB + m\angle ACB + m\angle CBA$. Subtract $m\angle CAB$ from both sides. Using the Subtraction Property of Equality:
$$
\begin{align*}
m\angle ZAB + m\angle CAB - m\angle CAB&=(m\angle CAB + m\angle ACB + m\angle CBA)-m\angle CAB\
m\angle ZAB&=m\angle ACB + m\angle CBA
\end{align*}
$$

# Answer:
The first blank is filled with “Linear Pair Postulate”, the second blank is filled with “Triangle Angle - Sum Theorem” and the third blank is filled with “Subtraction Property of Equality”

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Question

Explanation:

Step1: Linear Pair Postulate

Step2: Triangle Angle - Sum Theorem

Step3: Subtraction Property of Equality

Answer: