Question

1. which image would provide a good counterexample to the statement below? all supplementary angles form straight angles.

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles sum to \(180^\circ\). A straight angle is \(180^\circ\) and is formed by two angles on a straight line (adjacent, forming a linear pair). A counterexample would be supplementary angles not forming a straight angle (not adjacent, not on a straight line).

Step2: Analyze Each Image

• First Image: Angles \(35^\circ\) and \(55^\circ\). Sum: \(35 + 55 = 90^\circ\) (not supplementary).
• Second Image: Angles \(35^\circ\) and \(55^\circ\) (same as above, sum \(90^\circ\), not supplementary).
• Third Image: Angles \(55^\circ\) and \(125^\circ\). Sum: \(55 + 125 = 180^\circ\) (supplementary). These angles are not adjacent (not on a straight line), so they are supplementary but do not form a straight angle.
• Fourth Image: Angles \(125^\circ\) and \(55^\circ\) (sum \(180^\circ\)) but they are adjacent (on a straight line, forming a straight angle).

Answer:

The third image (with \(55^\circ\) and \(125^\circ\) angles, not adjacent)