Question

12.h.04d. thursday weekly bell work-september 18th
in the following figure, the two horizontal lines are parallel. which of the following does not equal 180°?

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary (add up to 180°), and vertical angles are equal.

Step2: Analyze angle pairs

• \(p\) and \(r\) are vertical angles, \(p = r\), and \(p + r\) is not necessarily 180°.
• \(p\) and \(t\) are consecutive - interior angles. Since the two horizontal lines are parallel, \(p + t=180^{\circ}\) (consecutive - interior angles are supplementary).
• \(q\) and \(s\) are vertical angles, \(q = s\), and \(q + s\) is not necessarily 180°.
• \(r\), \(u\), and \(t\) together form a straight - line. So \(r + u + t = 180^{\circ}\) (angles on a straight - line add up to 180°).

Answer:

\((p + r)^{\circ}\) and \((q + s)^{\circ}\) do not necessarily equal 180°. If we assume there are no other conditions given and we have to choose one option from the list (assuming the options are \(p + r\), \(p + t\), \(q + s\), \(r+u + t\)), the answer is \((p + r)^{\circ}\) (assuming \(p + t\) and \(r + u + t\) are among the other options as they equal 180° based on parallel - line and angle relationships).