Question

find ( mangle4 ).

Explanation:

Step1: Find \(m\angle2\)

Use the exterior - angle theorem. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle2=51^{\circ}-25^{\circ}=26^{\circ}\)

Step2: Find \(m\angle1\)

We know that the sum of angles in a triangle is \(180^{\circ}\). In the right - triangle with angle \(35^{\circ}\), \(m\angle1 = 90^{\circ}-35^{\circ}=55^{\circ}\)

Step3: Find \(m\angle5\)

In the triangle with angle \(28^{\circ}\), using the fact that the sum of angles in a triangle is \(180^{\circ}\) and the right - angle. \(m\angle5=90^{\circ}-28^{\circ}=62^{\circ}\)

Step4: Find \(m\angle6\)

Since the sum of angles around a point is \(180^{\circ}\) and considering the angles formed by the lines. \(m\angle6 = 180^{\circ}-(26^{\circ}+55^{\circ}+62^{\circ})=37^{\circ}\)

Step5: Find \(m\angle4\)

In the right - triangle with \(\angle6\), \(m\angle4=90^{\circ}-m\angle6\). Substitute \(m\angle6 = 37^{\circ}\), so \(m\angle4 = 53^{\circ}\)

Answer:

\(53^{\circ}\)