Question

find $m\angle6$.

Explanation:

Step1: Find \(m\angle5\)

The sum of angles in a triangle is \(180^{\circ}\). In the right - angled triangle with angle \(28^{\circ}\), \(\angle5=90^{\circ}-28^{\circ}\)

$$m\angle5 = 62^{\circ}$$

Step2: Find \(m\angle6\)

\(\angle5\) and \(\angle6\) form a linear pair (they are adjacent and supplementary). So \(m\angle6 = 180^{\circ}-m\angle5\)
Substitute \(m\angle5 = 62^{\circ}\) into the formula:

$$m\angle6=180^{\circ}-62^{\circ}=118^{\circ}$$

Answer:

\(118^{\circ}\)