Question

Ifn || m, find the value of x and the value of y.

A. y = 3.75 x = 11.25
B. y=4,x = 11
c. y = 5, x = 10
D. not enough information to determine
at the boot anewer from the choices provided

Answer 1

Answer: Option C

`y=5`,
`x=10`

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:

`(a)/(a')=(b)/(b') =(c)/(c')`

In this case

`a = 12\\a' = 4\\c = 15\\c' = y`

So:

`(12)/(4)=(15)/(y)`

Now solve the equation for the variable y

`3=(15)/(y)`

`y=(15)/(3)`

`y=5`

We know that

`x+y=15` and
`y=5`

Then

`x+5=15`

`x=10`

Finally the answer is:

`y=5`,
`x=10`