Question

find ( mangle 1 ).
(there are two triangles, triangle ( abc ) with ( angle a = 45^circ ), ( angle b = 80^circ ), and triangle ( sqr ) with ( angle 1 ) at ( r ), and some angle markings indicating possible congruence or similarity. then a box with ( mangle 1 = ) and the answer 55 checked.)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For \(\triangle ABC\), we find \(\angle C\).
\(m\angle C = 180^\circ - 45^\circ - 80^\circ\)

Step2: Calculate \(\angle C\)

\(m\angle C = 180 - 125 = 55^\circ\). Since \(\triangle ABC\) and \(\triangle SRQ\) are congruent (implied by angle markings), \(m\angle 1 = m\angle C = 55^\circ\).

Answer:

\(55^\circ\)