To find $m \angle 3$ in this figure, let's analyze the given information and proceed step-by-step. Here’s the breakdown:

1. Identify Known Angles and Relationships:

   • We are given:
     • $m \angle 1 = 51^\circ$
     • $m \angle 2 = 25^\circ$
     • $m \angle 5 = 28^\circ$
     • $m \angle 4 = 35^\circ$
   • Additionally, there are two right angles (indicated by the small squares), one adjacent to $\angle 1$ and one adjacent to $\angle 5$.

2. Applying Angle Sum Property in Triangles:

   • In the triangle containing $\angle 1$, $\angle 2$, and $\angle 3$, we can use the angle sum property. For any triangle, the sum of the internal angles is $180^\circ$.

3. Calculate $m \angle 3$:

   • Since we know $m \angle 1 = 51^\circ$ and $m \angle 2 = 25^\circ$: $m \angle 3 = 180^\circ - m \angle 1 - m \angle 2$ Substituting the known values: $m \angle 3 = 180^\circ - 51^\circ - 25^\circ$ $m \angle 3 = 180^\circ - 76^\circ = 104^\circ$

So, the measure of $\angle 3$ is $104^\circ$.

Would you like further details or explanations on any of the steps? Here are some related questions to deepen your understanding:

1. How can the angle sum property be applied to different polygons?
2. Why do the angles in a triangle always add up to $180^\circ$?
3. How does the presence of right angles influence calculations in geometric problems?
4. What methods are used to find unknown angles in polygons with more than three sides?
5. How can congruent triangles help in determining unknown angles?

Tip: In any geometric problem involving triangles, the angle sum property (that all angles add up to $180^\circ$) is a fundamental tool that can simplify many angle-finding tasks.