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In the diagram below, KLMN is a cyclic quadrilateral. Find the value of y.

Mathematics

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Answer

∠LNK\angle LNK

Step-by-step solution

2 steps

  1. Identify angles equal to yy.

    We are given ∠LMK=y\angle LMK = y. Angles subtended by the same arc at the circumference are equal.
    The arc LK subtends ∠LMK\angle LMK and ∠LNK\angle LNK.
    Therefore, ∠LNK=∠LMK\angle LNK = \angle LMK.

    8.2.1
    Another angle equal to yy is ∠LNK\angle LNK.
    Reason: Angles in the same segment (subtended by the same arc LK) are equal.

    ∠LNK\boxed{\angle LNK}

  2. Calculate the value of yy.

    KLMN is a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral sum to 180∘180^\circ.
    So, $\angle KNM + \

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