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kryton1212
 2 years ago
A student claims that if one of the interior angles of a parallelogram is 30, then it cannot be inscribed in a circle. Do you agree with him? Explain.
kryton1212
 2 years ago
A student claims that if one of the interior angles of a parallelogram is 30, then it cannot be inscribed in a circle. Do you agree with him? Explain.

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ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1We start with assuming that the parallelogram is inscribed in a circle. dw:1358656384414:dw Assume this to be a parallelogram ABCD

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1358656432945:dw Now angle A= angle C

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1A= C ( opposite angles of a parallelogram are equal)

kryton1212
 2 years ago
Best ResponseYou've already chosen the best response.1ohhh. parallelogram .... nothing then continue please

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1For a cyclic quadrilateral opposite angles sum should be 180, we have to satisfy this property also

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1so we have to have \[A=C=90\] this makes the parallelogram a rectangle, so any parallelogram which is inscribed in a circle is a rectangle

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1Therefore a parallelogram with one angle 30 can't be inscribed

kryton1212
 2 years ago
Best ResponseYou've already chosen the best response.1ok...how about one angle is 150 degrees? the opp. angle can be 30

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1But opposite angles of a parallelogram are equal,
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