Circles m and k are congruent, qr is congruent to ln and op is congruent to vw. find x and y.

Given, arc QR is congruent to arc LN and arc OP is congruent to arc VW.

And the expressions for each arc in the diagram also given as:

Arc QR = 2x - y, arc LN = 11 , arc OP= 10 and arc VW=5x+y.

Hence, we will get the system of equations as following:

Arc QR = Arc LN

2x - y = 11 ...(1)

Arc OP = Arc VW

5x + y = 10 ...(2)

Next step is to add the two equation to eliminate y so that we can solve the equations for x. Therefore,

2x+5x = 11 + 10

7x = 21

Divide each sides by 7.

So, x= 3

Now plug in x=3 in equation (2) to get the value of y.

5(3) + y = 10

15 + y =10

15 + y - 15 = 10 - 15 Subtracting 15 from each sides.

y = -5

So, x=3 and y =-5

i cant see the graph

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4