Answer :
Given:
In the given figure, [tex]\angle W\cong \angle T[/tex], 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,
[tex]\angle W\cong \angle T[/tex] (Given)
[tex]\angle WRS\cong \angle TRV[/tex] (Vertically opposite angles)
[tex]\triangle WRS\sim \triangle TRV[/tex] (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{WR}{WS}=\dfrac{RT}{VT}[/tex]
[tex]\dfrac{4x+3}{5}=\dfrac{7x+3}{8}[/tex]
[tex]8(4x+3)=5(7x+3)[/tex]
[tex]32x+24=35x+15[/tex]
Isolate the variable x.
[tex]24-15=35x-32x[/tex]
[tex]9=3x[/tex]
Divide both sides by 3.
[tex]\dfrac{9}{3}=x[/tex]
[tex]3=x[/tex]
Now,
[tex]WR=4x+3[/tex]
[tex]WR=4(3)+3[/tex]
[tex]WR=12+3[/tex]
[tex]WR=15[/tex]
And,
[tex]RT=7x+3[/tex]
[tex]RT=7(3)+3[/tex]
[tex]RT=21+3[/tex]
[tex]RT=24[/tex]
Therefore, the measure of WR is 15 units and the measure of RT is 24 units.