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 .

Answer 1

Answer:

Linear Pairs; triangle angle sum property; equality and subtraction property.

Step-by-step explanation:

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.

Answer 2

Answer:

We know that m∠ZAB + m∠CAB = 180° by the

✔ angle addition postulate

.

We also know m∠CAB + m∠ACB + m∠CBA = 180° because

✔ of the triangle angle sum theorem.

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

✔ subtraction property

.

Step-by-step explanation:

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