Question

find the measure of the numbered angle. 35 m∠7 = □°

Explanation:

Step1: Find the measure of ∠1

In a right - angled triangle, the sum of angles is \(180^{\circ}\). So, \(\angle1=180^{\circ}-90^{\circ}-40^{\circ}=50^{\circ}\)

Step2: Use the property of vertical angles

Since \(\angle1\) and \(\angle3\) are vertical angles, \(\angle3 = \angle1 = 50^{\circ}\)

Step3: Use the sum of angles in a quadrilateral - like figure (the figure with right angles)

In the figure with two right angles, the sum of angles around the intersection of lines: The sum of angles in a four - angled figure (where two angles are \(90^{\circ}\)) and using the fact that the sum of angles around a point formed by two intersecting lines. But more simply, note that \(\angle7\) and the non - right angle in the first triangle (the angle we found related steps) are in a "corresponding" or "parallel - line - like" (assuming some implicit parallelism from the figure structure) relationship. Another way: Consider the two right - angled triangles. The angles of the first triangle: \(40^{\circ},90^{\circ},50^{\circ}\). Since \(\angle3 = 50^{\circ}\) and using the property that \(\angle7\) is equal to the non - right, non - \(40^{\circ}\) angle of the first triangle (by the property of similar - triangle - like angle relationships in the figure structure)

Answer:

\(50\)