Question

AB and CD are two parallel lines intersected by a transversal EF. bisector of interior angles BPQ and DQP intersect at R. prove that angle PRQ is right angle

Answer 1

As, AB || CD
Sum of co -interior angles is 180°
angle BPQ + angle PQD = 180°
1/2 angle BPQ + 1/2 angle PQD = 90°
angle RPQ + angle PQR. = 90°

As, angle RPQ + PQR + PRQ. = 180°
90° + angle PRQ = 180°
angle PRQ = 90°

Answer 2

Answer:

90°.(PROVED)

Step-by-step explanation:

Given,

AB and CD are two parallel lines intersected by a transversal EF. bisector of interior angles BPQ and DQP intersect at R.

To Find,

Prove that the angle PQR is right angle.

As, AB || CD

Sum of co -interior angles is 180°

Angle BPQ + angle PQD = 180°

1/2 angle BPQ + 1/2 angle PQD = 90°

Angle RPQ + angle PQR. = 90°

As, angle RPQ + PQR + PRQ. = 180°

90° + angle PRQ = 180°

Angle PRQ = 90°

Hence, PROVED.

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