Answer: Option C
[tex]y=5[/tex], [tex]x=10[/tex]
Step-by-step explanation:
If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.
By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a', b', c' then:
[tex]\frac{a}{a'}=\frac{b}{b'} =\frac{c}{c'}[/tex]
In this case
[tex]a = 12\\a' = 4\\c = 15\\c' = y[/tex]
So:
[tex]\frac{12}{4}=\frac{15}{y}[/tex]
Now solve the equation for the variable y
[tex]3=\frac{15}{y}[/tex]
[tex]y=\frac{15}{3}[/tex]
[tex]y=5[/tex]
We know that
[tex]x+y=15[/tex] and [tex]y=5[/tex]
Then
[tex]x+5=15[/tex]
[tex]x=10[/tex]
Finally the answer is:
[tex]y=5[/tex], [tex]x=10[/tex]
