Question

Please help if you can​

Answer 1

Since OQ and RT are parallel lines, ∠QPS and ∠RSP are alternate interior angles. Alternate interior angles are congruent to each other, so ∠QPS must also be 129°.

• In the diagram, since lines
  `$OQ$` and
  `$RT$` are parallel, we know that corresponding angles
  `$\angle QPS$` and
  `$\angle RSP$` are congruent.
• Therefore,
  `$\angle RSP = \angle QPS = 129^\circ$`.
• Here's another way to think about it: imagine a transversal line (not shown in the diagram) that intersects both OQ and RT.
• This transversal would create two angle pairs:
  `$\angle QPS$` and
  `$\angle TSR$`, and
  `$\angle RSP$` and
  `$\angle TPQ$`.
• Since the transversal is perpendicular to both OQ and RT, these angle pairs would be vertical angles, and thus congruent. Therefore,
  `$\angle RSP = \angle TPQ = 129^\circ$`.