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Determine the value of the unknown angles or sides labelled as x or y in each of the diagram below.

Mathematics

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here are the solutions for questions 2 and 3.

Question 2: Determine the value of the unknown angles or sides labelled as xx or yy in each of the diagram below.

  1. Identify the given information.

    We are given two angles subtended by arcs:
    ∠RPS=5∘\angle RPS = 5^\circ
    ∠QTU=5∘\angle QTU = 5^\circ
    We are given the length of a chord: ST=15 cmST = 15 \text{ cm}.
    We need to find the value of yy, which is an angle, ∠PQR\angle PQR.

  2. Apply the theorem for angles subtended by the same arc.

    Angles subtended by the same arc at the circumference are equal

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