College

If OQ and RT are parallel lines, and [tex] m\angle QPS = 136^\circ [/tex], find the measure of angle RPS.

Answer :

Angle QPS and angle RTS are congruent, both measuring 136°. Additionally, since OQ and RT are parallel, angle PSQ and angle RTS are alternate interior angles and are also congruent.

If OQ and RT are parallel lines and m QPS = 136°, we can use the property that when a transversal intersects two parallel lines, the corresponding angles are congruent.

Therefore, angle QPS and angle RTS are congruent, both measuring 136°. Additionally, since OQ and RT are parallel, angle PSQ and angle RTS are alternate interior angles and are also congruent.

Hence, angle PSQ measures 136° as well. In summary, angles QPS, PSQ, and RTS all have a measure of 136°.

This is because when two lines are parallel and intersected by a transversal, the corresponding angles and alternate interior angles are congruent.

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The complete question is given below:

If OQ and RT are parallel lines and m QPS = 136°