Question

find the values of x and y.

x=

y=

Explanation:

Step1: Use the Angle - Angle - Side (AAS) congruence

Since the two triangles are congruent by AAS (two angles and a non - included side are equal). So, \(3x - 5=y + 12\) and \(5y-4=y + 12\).

Step2: Solve the equation for \(y\)

Solve \(5y-4=y + 12\).
Subtract \(y\) from both sides: \(5y-y-4=y - y+ 12\), \(4y-4 = 12\).
Add \(4\) to both sides: \(4y-4 + 4=12 + 4\), \(4y=16\).
Divide both sides by \(4\): \(y=\frac{16}{4}=4\).

Step3: Substitute \(y = 4\) into \(3x - 5=y + 12\)

Substitute \(y = 4\) into \(3x - 5=y + 12\), we get \(3x-5=4 + 12\).
Simplify the right - hand side: \(3x-5=16\).
Add \(5\) to both sides: \(3x-5 + 5=16+5\), \(3x=21\).
Divide both sides by \(3\): \(x=\frac{21}{3}=7\).

Answer:

\(x = 7\)
\(y = 4\)