Question

1. find m∠t.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle ABC\), we know two angles \(\angle A = 41^{\circ}\) and \(\angle B=74^{\circ}\). Let's first find \(\angle C\) in \(\triangle ABC\).

Step2: Calculate \(\angle C\) in \(\triangle ABC\)

Using the formula \(\angle A+\angle B+\angle C = 180^{\circ}\), we substitute the known values: \(\angle C=180^{\circ}-\angle A - \angle B\). So, \(\angle C=180^{\circ}-41^{\circ}-74^{\circ}=65^{\circ}\).

Step3: Assume \(\triangle ABC\cong\triangle RST\) (since no other information about the relationship between the two triangles is given, and we need to find \(\angle T\))

If \(\triangle ABC\cong\triangle RST\), then corresponding angles are equal. \(\angle T\) corresponds to \(\angle C\).

Answer:

\(m\angle T = 65^{\circ}\)