Question

directions: type your answer in the box.
what is the ( mangle mnt )?

Explanation:

Step1: Find the measure of ∠MTR

Since the sum of angles in a triangle - related context (external angle property or angle sum in a larger figure), but here we can note that ∠MTR is \(35^{\circ}+ 25^{\circ}=60^{\circ}\) (by the property of adjacent angles at point \(T\)).

Step2: Use the property of congruent triangles (SSS)

We know \(MT = RT\) (marked as equal), \(MN=RQ\) ( \(MN = 4\), \(RQ = 6 - 2=4\) assuming some segment - length relations from the figure's markings, and \(TN=TQ\) (perpendicular bisector or congruent segment markings). So, \(\triangle MNT\cong\triangle RQT\) (SSS - Side - Side - Side congruence criterion). Then \(\angle M=\angle R = 25^{\circ}\) (corresponding parts of congruent triangles).

Step3: Use the angle - sum property of a triangle in \(\triangle MNT\)

In \(\triangle MNT\), we know \(\angle M = 25^{\circ}\), \(\angle MTR = 60^{\circ}\) (from step 1, and since \(\triangle MNT\cong\triangle RQT\), the angle at \(T\) for \(\triangle MNT\) is half of \(\angle MTR\) if we consider the congruence and symmetry). Using the angle - sum property of a triangle (\(\angle M+\angle MNT+\angle NTM = 180^{\circ}\)). But another approach: since \(\triangle MNT\) has \(\angle M = 25^{\circ}\), and if we consider the fact that \(\angle MNT=180-(25 + 25)\) (using the property of isosceles triangle \(\triangle MNT\) (because \(MT = RT\) and \(\triangle MNT\cong\triangle RQT\) implies \(NT = QT\) and \(MN = RQ\))).
\(\angle MNT=130^{\circ}\)

Answer:

\(130\)