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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Given that PQRS is trapezium and PQ ∥SR AND PS∥QR
Let PQ is extended to T. Then, draw a line through R, which is parallel
to PS, intersecting PT at point T. It is clear that PTRS is a
parallelogram.
(i) PS = RT (Opposite sides of parallelogram PTRS are equal)
However, PS = QR (Given)
Therefore, QR = RT
∠RTQ = ∠RQT (Angle opposite to equal sides are also equal)
Consider the parallel lines PS and RT. PT is the transversal line for them..
∠P + ∠RTQ = 180º ( Sum of angles on the same side are equal to 180 )
∠P + ∠RQT = 180º (Using the relation ∠RTQ = ∠RQT ) ... (1)
However, ∠Q + ∠RQT = 180º (Linear pair angles) ... (2)
From equations (1) and (2), we obtain,
∠P = ∠Q.