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In the given figure, O is the centre of the circle PS = SO = PQ/2 and PM = MO, then find the difference between the measures of ∠QRS and ∠PQR. |
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Answer» O is the centre of the CIRCLE PS = SO = PQ/2 and PM = MOTO Find : difference between the measures of ∠QRS and ∠PQR.Solution:PQ is Diameter as it passes through CENTER O=> PO = RADIUS = Diameter/2 = PQ/2 PS = SO = PQ/2 Given => PS = SO = PO=> ∠POS = 60° ∠POS + ∠QOS = 180° Linear PAIR=> 60° + ∠QOS = 180° => ∠QOS = 120°∠QRS = (1/2) ∠QOS => ∠QRS = (1/2) 120°=> ∠QRS =60°in ΔPMS & ΔOMSPM = OM givenMS = MS commonPS = SO given => ΔPMS ≅ ΔOMS=> ∠PMS = ∠OMS ∠PMS + ∠OMS = 180°=> ∠PMS = ∠OMS = 90° ∠PMS = ∠RMQ ( vertically opposite angles)=> ∠RMQ = 90° in Δ QMR∠RMQ + ∠QRM + ∠MQR = 180°∠QRM = ∠QRS =60°∠MQR = ∠PQR=> 90° + 60° + ∠PQR = 180°=> ∠PQR = 30°difference between the measures of ∠QRS and ∠PQR. = 60° - 30° = 30°Learn More:difference between the measures of ∠QRS and ∠PQR.brainly.in/question/27331116brainly.in/question/27356073 |
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