Question

Analyze the diagram below and complete the instructions that follow.

Find the value of x and the value of y.

A.x = 15, y = 10
B.x = 20, y = 50
C.x = 50, y = 10
D.x = 50, y = 20
Answer is C x=50 y=10

Answer 1

Option C) x = 50, y = 10

Explanation:

We are given a two pairs of vertically opposite angle in the image.

Vertically opposite angle is formed when two lines intersect anf they are always equal.

Thus, we can write:

`3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240`

Solving the two equations in two variable, we get:

`x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50`

The value of x is 50 and y is 10.

Answer 2

C.
`x=50`,
`y=10`

Explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.

We know that when two line intersect each other, then vertical angles are congruent.

Using vertical angles theorem, we will get a system of equations as sown below:

`3y=x-20...(1)`

`5x-100=y+140...(2)`

From equation (1), we will get:

`x=3y+20`

Upon substituting this value in equation (2), we will get:

`5(3y+20)-100=y+140`

`5*3y+5*20-100=y+140`

`15y+100-100=y+140`

`15y=y+140`

`15y-y=y-y+140`

`14y=140`

`(14y)/(14)=(140)/(14)`

`y=10`

Therefore, the value of y is 10.

To find the value of x, we will substitute
`y=10` in equation (1) as:

`3*10=x-20`

`30=x-20`

`30+20=x-20+20`

`50=x`

Therefore, the value of x is 50 and option C is the correct choice.