Anonymous asked in Science & MathematicsMathematics · 1 month ago

Please help easy 10 points?? ?

Please help with number 14 i usually don’t like to do this but its due tomorrow and i wanna be able to understand 

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2 Answers

  • 1 month ago
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    The measure of <PQR is 90 degrees.  Segment PR appears to be a diameter of the circle, and any triangle inscribed in a circle, with the diameter as one side, turns out to be a right triangle.  (A famous theorem, I forget what it's called.)  The 100 degrees is completely irrelevant!

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  • 1 month ago

    Since O is in the center, it follows that OP = OR = OQ = r where r is the radius of the circle. Therefore, POQ and OQR are isosceles triangles. Make note that since <POQ = 100 degrees that <QOR = 80 degrees. It follows that <OPQ = <PQO = 40 degrees. Similarly, <OQR = <ORQ = 50 degrees.In conclusion, <PQR = <PQO + <OQR = 40 + 50 = 90 degrees.

    In particular, az lander, the angle isn't completely irrelevant because, presumably, the angle would be a requirement in proving the theorem you stated. If not, at minimum, the 100 allows for one to solve the problem without any theorems.

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