Question

which of the following is incorrect? x + y = 180° y + z = 180° a = z c = b

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, corresponding angles are equal, vertical angles are equal, and adjacent angles on a straight - line sum to 180°.

Step2: Analyze each option

• For \(x + y=180^{\circ}\), \(x\) and \(y\) are adjacent angles on a straight - line formed by the transversal, so \(x + y = 180^{\circ}\) is correct.
• For \(a = z\), \(a\) and \(z\) are corresponding angles, so \(a = z\) is correct.
• For \(c = b\), \(c\) and \(b\) are vertical angles, so \(c = b\) is correct.
• For \(y+z = 180^{\circ}\), \(y\) and \(z\) are neither adjacent angles on a straight - line nor supplementary in any other way based on the parallel - line and transversal relationship. So \(y + z=180^{\circ}\) is incorrect.

Answer:

\(y + z = 180^{\circ}\) is incorrect.