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

Question

anonymous · Answer

attachment

anonymous · Answer

Will give medal! help please!

anonymous · Answer

@RadEn  can I please get help

raden · Answer

hint :
O + Q = 180

raden · Answer

so,
x+16+6x-4 = 180
solve for x, first

raden · Answer

got it ?

anonymous · Answer

not really so do i combine like terms

raden · Answer

yes, combine the like terms then solve for x. what do you get ?

anonymous · Answer

I got 26 but I think I did it wrong

raden · Answer

x+16+6x-4 = 180
7x + 12 = 180
7x = 180 - 12
7x = 168
x = 168/7 = 24

anonymous · Answer

So thats my final answer?

raden · Answer

no, that is a start :)

anonymous · Answer

oh ok can you help me with the other step please

anonymous · Answer

and thank for not juts giving me the answer.......I want to learn how to do it to

raden · Answer

look at the diagram once again. we knowed that O + Q = 180, and
P + R = 180 too

anonymous · Answer

yeah I can se it

raden · Answer

known R = 2x + 16
we have x = 24, so distribute x = 24 into equation of R, first.

R = 2x + 16 = 2(24) + 16 = 48 + 16 = 64

raden · Answer

recall that :

P + R = 180
P + 64 = 180
P = 180 - 64
P = 116

raden · Answer

P is as the measure of OPQ. so, OPQ = 116
hope that make sense

anonymous · Answer

Thank you,can you help me with some questions from my test please.......I am very confused

raden · Answer

anonymous · Answer

No its like diffrent questions