Question

find the m∠1. m∠1 = degrees

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: \(\angle A = 45^{\circ}\) and \(\angle B=80^{\circ}\). Let's first find \(\angle C\).
\[180^{\circ}=\angle A+\angle B+\angle C\]
\[ \angle C=180^{\circ}-\angle A - \angle B\]
\[ \angle C=180^{\circ}-45^{\circ}-80^{\circ}=55^{\circ}\]

Step2: Assume \(\triangle ABC\) and \(\triangle RQS\) are similar (if no other information about the relationship between the triangles is given, and we assume they are related in a way that corresponding angles are equal).

If \(\angle C\) and \(\angle 1\) are corresponding angles, then \(m\angle1 = 55^{\circ}\)

Answer:

55