Question

help for fan and medal

Answer 1

Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠PQR?

Answer 2

41
67
113
139

Answer 3

I want to know how to do this not just have the answer

Answer 4

Google it lol sorry😂

Answer 5

@derek_ortiz I already have and everyones saying different things

Answer 6

@bme89 do you know this?

Answer 7

hmmm, well 360 = x+17 + 2x+19 + 6x-5 + angle at P

Answer 8

Im still very confused, what does that mean?

Answer 9

The sum of the 4 angles will always equal 360 for a quadrilateral...
Angle RQP is obtuse, so it cannot be either of the first 2 options.

Answer 10

okay im thinking 113

Answer 11

Is the angle of P given??

Answer 12

nope

Answer 13

now what?

Answer 14

Okay, so since it is inscribed within the circle, you can tell that angle PQR is larger than angle at P. If we calculate the angle at P based on the last 2 choices, we get 152 or 128... The 152 doesn't make sense because that would be larger than angle PQR. 128 at P would be less than the angle at PQR (139)

Answer 15

so then D?

Answer 16

Yes

Answer 17

that was right. THANK YOU!

Answer 18

You are most welcome! It was a tricky problem because it cannot be calculated directly...