In a trapezium PQRS, PQ∥RS. Calculate ∠R if ∠P = 72° and ∠Q = 54°.
126°
In trapezium PQRS with PQ∥RS, QR is a transversal of the parallel sides, so ∠Q and ∠R are co-interior angles and add up to 180°.
So ∠R = 180° – ∠Q = 180° – 54° = 126°.
Similarly ∠S = 180° – ∠P = 180° – 72° = 108°.
Check: ∠P + ∠Q + ∠R + ∠S = 72° + 54° + 126° + 108° = 360°, the angle sum of a quadrilateral.
Hence, 126°.
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