## 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.

1. ash2326

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

2. kryton1212

yes

3. ash2326

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

4. kryton1212

why they are equal?

5. ash2326

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

6. kryton1212

isn't that A+C=180?

7. kryton1212

ohhh. parallelogram .... nothing then continue please

8. ash2326

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

9. kryton1212

ok...

10. ash2326

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

11. kryton1212

and then>

12. ash2326

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

13. kryton1212

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

14. ash2326

But opposite angles of a parallelogram are equal,

15. kryton1212

ohhh yes..

16. kryton1212

thank you so much

17. ash2326

Welcome :D