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.

Question

ash2326 · Answer

We start with assuming that the parallelogram is inscribed in a circle.
|dw:1358656384414:dw|
Assume this to be a parallelogram ABCD

anonymous · Answer

yes

ash2326 · Answer

|dw:1358656432945:dw|
Now angle A= angle C

anonymous · Answer

why they are equal?

ash2326 · Answer

A= C ( opposite angles of a parallelogram are equal)

anonymous · Answer

isn't that A+C=180?

anonymous · Answer

ohhh. parallelogram .... nothing then
continue please

ash2326 · Answer

For a cyclic quadrilateral opposite angles sum should be 180, we have to satisfy this property also

anonymous · Answer

ok...

ash2326 · Answer

so 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

anonymous · Answer

and then>

ash2326 · Answer

Therefore a parallelogram with one angle 30 can't be inscribed

anonymous · Answer

ok...how about one angle is 150 degrees? the opp. angle can be 30

ash2326 · Answer

But opposite angles of a parallelogram are equal,

anonymous · Answer

ohhh yes..

anonymous · Answer

thank you so much

ash2326 · Answer

Welcome :D