Question

Answer and I will give you brainiliest ​

Answer 1

Given:

In the given figure,
`\angle W\cong \angle T`, WS = 5, WR = 4x+3, RT=7x+3 and VT=8.

To find:

The measure of WR and RT.

Solution:

In triangles WRS and TRV,

`\angle W\cong \angle T` (Given)

`\angle WRS\cong \angle TRV` (Vertically opposite angles)

`\triangle WRS\sim \triangle TRV` (AA property of similarity)

We know that the corresponding sides of similar triangles are proportional. So,

`(WR)/(WS)=(RT)/(VT)`

`(4x+3)/(5)=(7x+3)/(8)`

`8(4x+3)=5(7x+3)`

`32x+24=35x+15`

Isolate the variable x.

`24-15=35x-32x`

`9=3x`

Divide both sides by 3.

`(9)/(3)=x`

`3=x`

Now,

`WR=4x+3`

`WR=4(3)+3`

`WR=12+3`

`WR=15`

And,

`RT=7x+3`

`RT=7(3)+3`

`RT=21+3`

`RT=24`

Therefore, the measure of WR is 15 units and the measure of RT is 24 units.