Question

1. given triangle nml is congruent to triangle rts, find the value of x? 21____ type the value on your screen in euphoria.

Explanation:

Step1: Find the measure of angle \(M\)

In \(\triangle NML\), using the angle - sum property of a triangle (\(\angle N+\angle L+\angle M = 180^{\circ}\)).
Substitute \(\angle N = 55^{\circ}\) and \(\angle L=65^{\circ}\) into the formula:
\(\angle M=180^{\circ}-(55^{\circ}+65^{\circ})\)
\(\angle M = 180^{\circ}-120^{\circ}=60^{\circ}\)

Step2: Use the congruence property

Since \(\triangle NML\cong\triangle RTS\), then \(\angle M=\angle T\) (corresponding angles of congruent triangles are equal).
Set up the equation \(2x + 30=60\)

Step3: Solve for \(x\)

Subtract \(30\) from both sides of the equation \(2x+30 - 30=60 - 30\)
\(2x=30\)
Divide both sides by \(2\): \(x=\frac{30}{2}\)

Answer:

\(15\)