if np bisects mnq, mnq= (8x+12), pnq=78 and rnm=(3y-9), find the values of x and y

Answer 1

Without a diagram, we just all scratch our heads. Especially if there's an error. I think you MAY have meant ∠PNM = 3y - 9 and I'm guessing that a diagram looks like this:

If my guesses are correct then (since segment NP bisects ∠MNQ) then 3y - 9 = 78:

3y - 9 = 78

3y = 87

y = 29

Since the measure ∠MNP = the measure of ∠PNQ, they are both equal to 78° making the measure of ∠MNQ = 78•2 = 156°, therefore 8x + 12 = 156:

8x + 12 = 156

8x = 144

x = 18