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,

$\dfrac{WR}{WS}=\dfrac{RT}{VT}$

$\dfrac{4x+3}{5}=\dfrac{7x+3}{8}$

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

$32x+24=35x+15$

Isolate the variable x.

$24-15=35x-32x$

$9=3x$

Divide both sides by 3.

$\dfrac{9}{3}=x$

$3=x$

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.