Question

which of the following pairs of angles does not add up to 180°?

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, certain angle - pairs add up to 180°. Supplementary angle pairs include same - side interior angles and same - side exterior angles.

Step2: Analyze each pair

• For a and w: They are same - side interior angles, so \(a + w=180^{\circ}\).
• For c and d: They are a linear pair. A linear pair of angles is supplementary, so \(c + d = 180^{\circ}\).
• For x and w: They are vertical angles. Vertical angles are equal (\(x = w\)) and do not add up to 180° (except when \(x=w = 90^{\circ}\), but not in general).
• For c and y: They are same - side exterior angles, so \(c + y=180^{\circ}\).

Answer:

x and w