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yeval76

  • one year ago

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠OPQ?

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  1. yeval76
    • one year ago
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  2. anonymous
    • one year ago
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    Remember that if a quadrilateral is inscribed in a circle, the opposite angles sum up 180 degrees

  3. anonymous
    • one year ago
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    So, if you sum ROP + PQR = 180

  4. anonymous
    • one year ago
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    ROP=x+16 and PQR=6x-4, so ROP+PQR=x+16+6x-4=180

  5. anonymous
    • one year ago
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    x+16+6x-4 = 7x+12 = 180, can you do this?

  6. yeval76
    • one year ago
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    I got 12=12=180 @Natriumhydrid

  7. anonymous
    • one year ago
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    Quadrilaterals add up to 360, so couldn't you add all of the equations (angle p=x) and set them equal to 360

  8. anonymous
    • one year ago
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    (x+16) + (2x+16) + (6x-4) + x =360 angle P=x

  9. yeval76
    • one year ago
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    I know that the opposite angles in a inscribed quadrilateral are supplementary.

  10. yeval76
    • one year ago
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    So x=83 @Katherine2016

  11. yeval76
    • one year ago
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    Do we apply that x to all the equations around the circle? @Katherine2016

  12. anonymous
    • one year ago
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    how do you get 12=12=180?

  13. yeval76
    • one year ago
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    Omg I didn't put the answer choices: m∠OPQ + (2x + 16)° = 180° m∠OPQ = (6x − 4)° + (2x + 16)° m∠OPQ + (x + 16)° + (6x − 4)°= 360° m∠OPQ = (x + 16)° + (6x − 4)°

  14. yeval76
    • one year ago
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    I think its the first one?

  15. yeval76
    • one year ago
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    Because, since the opposite angles are supplementary, they would equal 180 so angle OPQ plus its opposite angle which is (2x+16) would be 180...

  16. yeval76
    • one year ago
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    Am I right?

  17. anonymous
    • one year ago
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    7x+12 = 180 7x = 168 x=24, so the x in the image is 24, replacing in ∠ORQ we get ∠ORQ=64, so ∠OPQ must be supplementary then ∠OPQ=116

  18. anonymous
    • one year ago
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    The correct is A

  19. yeval76
    • one year ago
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    Can you help me with another question? @Natriumhydrid

  20. yeval76
    • one year ago
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    Thank you again!

  21. anonymous
    • one year ago
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    ya

  22. yeval76
    • one year ago
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    The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X: What is the measure of angle ACB?

  23. anonymous
    • one year ago
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    OK, so, if angle ABX=42, then the arc AX=84 (because is inscribed angle), and the arc AB=100, now using the formula of external angle, angle ACB=(100-84)/2=16/2=8, so ACB=8degrees

  24. yeval76
    • one year ago
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    Omg again! I forgot to put the answer choices! 29° 8° 16° 21°

  25. anonymous
    • one year ago
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    is 8 degrees :)

  26. yeval76
    • one year ago
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    Thanks! @Natriumhydrid

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