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21 February, 00:57

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.

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Answers (2)
  1. 21 February, 01:19
    0
    A: angle addition postulate

    B: of the triangle sum theorem

    C. subtraction property

    Just did the assignment
  2. 21 February, 01:24
    0
    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.
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