Circles M and K are congruent, QR ≅ LN and OP ≅ VW . Find x and y.

Base in your question where there is a diagram that shows a circle M and K are congruent and QR is congruent to LN and OP is congruent to VW so calculate the value of X and Y if the given is in the diagram.So the answer would be X= 2 and Y=4

Answer Link

ApusApus ApusApus · Answer 2 · 2025-03-26T05:16:54-04:00

Answer:

[tex]x=4[/tex]

[tex]y=2[/tex]

Step-by-step explanation:

We have been given two congruent circles. We are asked to find the value of x and y.

We have been given that [tex]OP\cong VW[/tex]. This means [tex]OP=VW[/tex].

Upon substituting our given values, we will get:

[tex]3x-y=10...(1)[/tex]

We have been given that [tex]QR\cong LN[/tex]. This means [tex]QR=LN[/tex].

Upon substituting our given values, we will get:

[tex]x+y=6...(2)[/tex]

From equation (2), we will get:

[tex]x=6-y[/tex]

Upon substituting this value in equation (1), we will get:

[tex]3(6-y)-y=10[/tex]

[tex]18-3y-y=10[/tex]

[tex]18-4y=10[/tex]

[tex]18-18-4y=10-18[/tex]

[tex]-4y=-8[/tex]

[tex]\frac{-4y}{-4}=\frac{-8}{-4}[/tex]

[tex]y=2[/tex]

Therefore, the value of y is 2.

Now, we will substitute [tex]y=2[/tex] in equation (2) to solve for x.

[tex]x+2=6[/tex]

[tex]x+2-2=6-2[/tex]

[tex]x=4[/tex]

Therefore, the value of x is 4.