Question

Given triangle ABC, with exterior angle ∠ZAB formed by the extension of side AC, and ∠CAB being a linear pair with ∠ZAB. If ∠CAB = ∠ACB, what can be concluded about the angles ∠ZAB, ∠ACB, and ∠CBA?

a) ∠ZAB = ∠ACB = ∠CBA
b) ∠ZAB = ∠ACB ≠ ∠CBA
c) ∠ZAB ≠ ∠ACB = ∠CBA
d) ∠ZAB ≠ ∠ACB ≠ ∠CBA

Answer 1

The angles ∠ZAB, ∠ACB, and ∠CBA are all equal.

Step-by-step explanation:

Given triangle ABC, with exterior angle ∠ZAB formed by the extension of side AC, and ∠CAB being a linear pair with ∠ZAB. If ∠CAB = ∠ACB, we can conclude that:

1. ∠ZAB = ∠ACB = ∠CBA
2. ∠ZAB = ∠ACB ≠ ∠CBA
3. ∠ZAB ≠ ∠ACB = ∠CBA
4. ∠ZAB ≠ ∠ACB ≠ ∠CBA

Therefore, the correct answer is option a) ∠ZAB = ∠ACB = ∠CBA.