Question:
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
The image of the degrees of angles is attached below:
Answer:
Option C: [tex]x=50, y=10[/tex] is the value of x and y
Explanation:
Since, we know that the vertically opposite angles are equal.
From the figure, the angles [tex]3y[/tex] and [tex]x-20[/tex] are equal.
[tex]3y=x-20[/tex]
[tex]3y+20=x[/tex] -----------(1)
And the angles [tex]y+140[/tex] and [tex]5x-100[/tex] are equal.
[tex]y+140=5x-100[/tex]
[tex]y=5x-240[/tex] -----------(2)
Substituting [tex]x=3y+20[/tex] in the equation [tex]y=5x-240[/tex] , we get,
[tex]y=5(3y+20)-240[/tex]
[tex]y=15y+100-240[/tex]
[tex]y=15y-140[/tex]
[tex]-14y=-140[/tex]
[tex]y=10[/tex]
Thus, the value of y is [tex]y=10[/tex]
Substituting [tex]y=10[/tex] in the equation [tex]3y+20=x[/tex] , we have,
[tex]3(10)+20=x[/tex]
[tex]30+20=x[/tex]
[tex]50=x[/tex]
Thus, the value of x is [tex]x=50[/tex]
Therefore, the value of x and y are [tex]x=50[/tex] and [tex]y=10[/tex]
Hence, Option C is the correct answer.
