Question

find ( mangle6 ).

Explanation:

Step1: Find \(m\angle3\)

Using the exterior - angle theorem for the first triangle: \(m\angle3=51^{\circ}-25^{\circ}=26^{\circ}\)

Step2: Find \(m\angle2\)

Since the sum of angles in a triangle is \(180^{\circ}\), and we assume the right - angled triangle properties (implicit from the figure's right angles). But more directly, if we consider the next part. Wait, another approach:
We know that in the right - angled triangle with angle \(28^{\circ}\) and the right - angle (\(90^{\circ}\)) in the larger structure. First, note that \(\angle5 = 90^{\circ}-28^{\circ}=62^{\circ}\) (because in a right - triangle, the two non - right angles are complementary)

Step3: Find \(m\angle6\)

Since the triangle containing \(\angle4,\angle5,\angle6\) is a right - triangle (as there is a right - angle in the figure related to it). And we know that in a right - triangle, if one non - right angle is \(\angle5 = 62^{\circ}\), then \(\angle6=90^{\circ}-62^{\circ}=28^{\circ}\)

Answer:

\(28^{\circ}\)