Question

These two trapezoids are similar. In both trapezoids, the left and right sides are not parallel. Find the values of x,y,z,j, and k

Explain your answers.
PLEASE HELP ME :)

Answer 1

Part 1)
`x=10\ units`

Part 2)
`y=4.5\ units`

Part 3)
`z=7.5\ units`

Part 4)
`m<j=140\°`

Part 5)
`m<k=72\°`

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

so

`(y)/(3)=(6)/(4)=(z)/(5)=(15)/(x)`

step 1

Find the measure of x

`(6)/(4)=(15)/(x)`

`x=4*15/6=10\ units`

step 2

Find the measure of y

`(y)/(3)=(6)/(4)`

`y=3*6/4=4.5\ units`

step 3

Find the measure of z

`(6)/(4)=(z)/(5)`

`z=5*6/4=7.5\ units`

step 4

Find the measure of angle j

we know that

The corresponding angles are congruent

In this part

`m<j+40\°=180\°` -----> by consecutive interior angles (supplementary angles)

so

`m<j=180\°-40\°=140\°`

step 5

Find the measure of angle k

we know that

`m<k=72\°` ------> by corresponding angles