anonymous
  • anonymous
Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.
Mathematics
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anonymous
  • anonymous
Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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campbell_st
  • campbell_st
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|
campbell_st
  • campbell_st
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
campbell_st
  • campbell_st
|dw:1434749343513:dw| so you need this diagram

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campbell_st
  • campbell_st
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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