PQRS is a parallelogram. Find ∠z\angle z.

Properties and criteria of parallelogramsRecognising angles and their sizes中文
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Worked solution

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1. Find the interior angle at S

Interior ∠PSR=360∘−288∘=72∘\text{Interior } \angle PSR = 360^\circ - 288^\circ = 72^\circ (angles at a point)

2. Find angle z using the properties of a parallelogram

∠z=180∘−72∘=108∘\angle z = 180^\circ - 72^\circ = 108^\circ (interior angles, PS∥QRPS \parallel QR)

Answer

108∘108^\circ

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