Question

find $m\angle4$.

Explanation:

Step1: Find \(m\angle3\)

Using the exterior - angle property of a triangle (an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles). For the triangle with angles \(25^{\circ}\) and \(51^{\circ}\), \(m\angle3=51^{\circ}-25^{\circ} = 26^{\circ}\)

Step2: Analyze the right - angled triangle with \(\angle1\)

In a right - angled triangle (the right - angled triangle with \(\angle1\) and \(35^{\circ}\)), since the sum of angles in a triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\), \(m\angle1 = 90^{\circ}-35^{\circ}=55^{\circ}\)

Step3: Analyze the right - angled triangle with \(\angle6\)

In the right - angled triangle with \(28^{\circ}\) and \(\angle6\), \(m\angle6=90^{\circ}-28^{\circ} = 62^{\circ}\)

Step4: Find \(m\angle4\)

In the right - angled triangle with \(\angle4\) and \(\angle6\), since the sum of angles in a triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\), \(m\angle4=90^{\circ}-62^{\circ}=28^{\circ}\)

Answer:

\(28\)