Question

use the following diagram for the following questions. given \\( \triangle rws \cong \triangle tuv \\), determine the values of \\( x \\) and \\( y \\). 11 fill in the bl x 1 point \\( x= \\) type your answer... 12 fill in the blank 1 point \\( y= \\) type your answer...

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle RWS\cong\triangle TUV\), corresponding angles and sides are equal.
For angles: \(\angle R=\angle U\). Given \(\angle R=(8x - 22)^{\circ}\) and \(\angle U = 40^{\circ}\), so \(8x-22 = 40\).

Step2: Solve the equation for \(x\)

Add \(22\) to both sides of the equation \(8x-22 = 40\): \(8x=40 + 22\), \(8x=62\). Then divide both sides by \(8\): \(x=\frac{62}{8}=\frac{31}{4}=7.75\).

Step3: Use the property of congruent sides

For sides: \(WS = UV\). Given \(WS = 20\) and \(UV=2y + 1\), so \(2y+1=20\).

Step4: Solve the equation for \(y\)

Subtract \(1\) from both sides of the equation \(2y + 1=20\): \(2y=20 - 1\), \(2y=19\). Then divide both sides by \(2\): \(y=\frac{19}{2}=9.5\).

Answer:

\(x = 7.75\)
\(y=9.5\)