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anonymous

  • one year ago

Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.

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  1. campbell_st
    • one year ago
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    this is really straight forward if you know about circle geometry in particular the property " the angle at the centre is double the angle at the circumference, standing on the same arc" it looks like |dw:1434749178035:dw|

  2. campbell_st
    • one year ago
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    so you are being asked to prove a quadrilateral is cyclic |dw:1434749258555:dw| mark the centre as O start by joining SO and RO

  3. campbell_st
    • one year ago
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    |dw:1434749343513:dw| so you need this diagram

  4. campbell_st
    • one year ago
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    then the proof is Let angle STR = y angle SWR = x reflex angle SOR = 2y (angle at the centre double the angle at the circumference standing on the same arc SWR) Obtuse angle SOR = 2x (angle at the centre double the angle at the circumference standing on the same arc STR) then Reflex angle SOR + obtuse angle SOR = 360 ( 2 angles form a revolution) therefore 2x + 2y = 360 divide by 2 x + y = 180 therefore angle STR + SWR = 180 ( supplementary angles) hope it makes sense

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