Question

FAN + MEDAL!!
The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

The four angles of the quadrilateral are (35, 45, or 85) degrees, (75,85, or 90) degrees, (115, 125, or 135) degrees, and (105, 115, or 125) degrees, respectively.

Answer 1

I'd suggest you draw this situation.
Caution: Your problem statement mentions "4 angles," but your answer choices involve only 3 angles. How could that be?

Answer 2

Those are the drop down options, theres 4 different questions, the numbers in parenthesis are the multiplication answers i need to pick one of each

Answer 3

"The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4." The trick here is to add up those four numbers to get the sum S.

Then the 1 corresponds to 1/S of the circle's circumference; the 2 corresponds to 2/S, etc.

Find S and write out the other 2 fractions (corresponding to 5 and 4).

Answer 4

The sum of S = 12?
5/12
4/12

Answer 5

very good. Now, as a check, add up 1/12, 2/12, 5/12 and 4/12.

Answer 6

= 1

Answer 7

that shows that our math is correct. :)

Answer 8

How many degrees constitute 1 complete circle?

Answer 9

360

Answer 10

right. Now please take that 1/12 and multiply 360 degrees by it.

Answer 11

=30

Answer 12

Good. Please calculate the remaining 3 central angles.

Answer 13

1/12*360 = 30 and thats not an option?
2/12*360 = 60 and thats not an option either

Answer 14

In that case: "The four angles of the quadrilateral" ... we may have to explore options other than "central angles." Taking that 30 degree angle as an example: it corresponds to a central angle of 30 degrees. Perhaps by "The four angles of the quadrilateral" some other angles are involved, not the central angles. In this case, I don't yet know what to tell you. Have you considered drawing the quadrilateral?

Answer 15

No i havent its really confusing

Answer 16

It's OK to draw the central angles. But there's another interpretation of "The four angles of the quadrilateral:" Draw four lines connecting the four points on the circle that we found earlier.