Question

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠OPQ?

Answer 1

Remember that if a quadrilateral is inscribed in a circle, the opposite angles sum up 180 degrees

Answer 2

So, if you sum ROP + PQR = 180

Answer 3

ROP=x+16 and PQR=6x-4, so ROP+PQR=x+16+6x-4=180

Answer 4

x+16+6x-4 = 7x+12 = 180, can you do this?

Answer 5

I got 12=12=180 @Natriumhydrid

Answer 6

Quadrilaterals add up to 360, so couldn't you add all of the equations (angle p=x) and set them equal to 360

Answer 7

(x+16) + (2x+16) + (6x-4) + x =360
angle P=x

Answer 8

I know that the opposite angles in a inscribed quadrilateral are supplementary.

Answer 9

So x=83 @Katherine2016

Answer 10

Do we apply that x to all the equations around the circle? @Katherine2016

Answer 11

how do you get 12=12=180?

Answer 12

Omg I didn't put the answer choices:

m∠OPQ + (2x + 16)° = 180°
m∠OPQ = (6x − 4)° + (2x + 16)°
m∠OPQ + (x + 16)° + (6x − 4)°= 360°
m∠OPQ = (x + 16)° + (6x − 4)°

Answer 13

I think its the first one?

Answer 14

Because, since the opposite angles are supplementary, they would equal 180 so angle OPQ plus its opposite angle which is (2x+16) would be 180...

Answer 15

Am I right?

Answer 16

7x+12 = 180
7x = 168
x=24, so the x in the image is 24, replacing in ∠ORQ we get ∠ORQ=64, so ∠OPQ must be supplementary then ∠OPQ=116

Answer 17

The correct is A

Answer 18

Can you help me with another question? @Natriumhydrid

Answer 19

Thank you again!

Answer 20

ya

Answer 21

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X:

What is the measure of angle ACB?

Answer 22

OK, so, if angle ABX=42, then the arc AX=84 (because is inscribed angle), and the arc AB=100, now using the formula of external angle, angle ACB=(100-84)/2=16/2=8, so ACB=8degrees

Answer 23

Omg again! I forgot to put the answer choices!

29°
8°
16°
21°

Answer 24

is 8 degrees :)

Answer 25

Thanks! @Natriumhydrid