Question

question 7
solve for x and y.
x =
and y =
given δrws ≅ δtuv, find the values of x and y.
(image of two triangles: δrws with right angle at w, sides 15, 20, 25, angle at r: (8x - 27)°; δtuv with angle at v: 29°, side tv: 3y + 7)

Explanation:

Step1: Use the property of congruent triangles (corresponding angles are equal)

Since \(\triangle RWS\cong\triangle TUV\), then \(\angle R=\angle V\).
We have the equation \(8x - 27=29\).
Add \(27\) to both sides: \(8x=29 + 27\), so \(8x=56\).
Divide both sides by \(8\): \(x=\frac{56}{8}=7\).

Step2: Use the property of congruent triangles (corresponding sides are equal)

Since \(\triangle RWS\cong\triangle TUV\), then \(WS = UV\).
We know \(WS = 20\) and \(UV=3y + 7\).
Set up the equation \(3y+7 = 20\).
Subtract \(7\) from both sides: \(3y=20 - 7\), so \(3y=13\).
Divide both sides by \(3\): \(y=\frac{13}{3}\).

Answer:

\(x = 7\) and \(y=\frac{13}{3}\)