Question

Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to arc VW. Find x.

Answer 1

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)

We need to find the value of x. So, we can add the equations to eliminate y so that we can solve the equations for x. Therefore,

2x+5x = 11 + 10

7x = 21

$\frac{7x}{7} =\frac{21}{7}$ Divide each sides by 7.

So, x= 3