Question

11/14 - triangle congruence schoology assignment
let \\( \triangle a b c \cong \triangle d e f \\). find \\( m \angle e \\).
\\( m \angle e= \\)

Explanation:

Step1: Find the value of \(x\)

Since \(\triangle ABC\cong\triangle DEF\), \(AC = DF\). So \(3x + 33=5x + 5\).
Subtract \(3x\) from both sides: \(33 = 2x+5\).
Subtract \(5\) from both sides: \(28 = 2x\).
Divide both sides by \(2\): \(x = 14\).

Step2: Find the value of \(y\)

Since \(\triangle ABC\cong\triangle DEF\), \(\angle B=\angle E\). So \(101 + y=6y-24\).
Subtract \(y\) from both sides: \(101=5y - 24\).
Add \(24\) to both sides: \(125 = 5y\).
Divide both sides by \(5\): \(y = 25\).

Step3: Calculate \(m\angle E\)

Substitute \(y = 25\) into \(6y-24\): \(6\times25-24\).
First, calculate \(6\times25 = 150\).
Then, \(150-24=126\).

Answer:

\(126^{\circ}\)