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

Answer:

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

Step-by-step 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:

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

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

$15y+100-100=y+140$

$15y=y+140$

$15y-y=y-y+140$

$14y=140$

$\frac{14y}{14}=\frac{140}{14}$

$y=10$

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.

Answer 2

Answer:

Option C) x = 50, y = 10

Step-by-step 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.