Question

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 .

Answer 1

Answer:

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.

Answer 2

Answer:

angle addition postulate

of the triangle angle sum theorem

subtraction property

.

Step-by-step explanation:

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