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7 September, 18:47

What is the measure of ∠spq in this rhombus? m∠spr = (2x+15) ° m∠qpr = (3x-5) ° enter your answer in the box?

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  1. 7 September, 20:44
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    A rhombus is a quadrilateral with fours sides that are equal. The diagonals of a rhombus bisect the angles. In this case PR is a diagonal, such that ∠SPQ is bisected, therefore ∠ SPR = ∠QPR

    Thus, 2x + 15 = 3x-5

    solving for the value of x,

    x=20

    Then, ∠SPR = 2 (20) + 15 = 55 and ∠ QPR = 3 (20) - 5 = 55

    Therefore, ∠SPQ = ∠SPR + ∠QPR

    = 55 + 55 = 110

    Hence, the answer is 110
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