To find the value of angle $k$ in the given diagram, we can use geometric principles involving triangles and angles around points. Here is the step-by-step process:

Step 1: Interior Angles in the Triangle

The sum of interior angles in any triangle is $180^\circ$. In this case, the triangle is formed by the angles $62^\circ$, $79^\circ$, and $k$. Therefore, we can set up the equation:

$62^\circ + 79^\circ + k = 180^\circ$

Step 2: Solve for $k$

$141^\circ + k = 180^\circ$

$k = 180^\circ - 141^\circ$

$k = 39^\circ$

Thus, the size of the angle marked $k$ is $39^\circ$.

Would you like more details or have further questions? Here are five questions to expand on this:

1. What is the formula for finding the sum of the interior angles of any polygon?
2. How do we find the exterior angle of a triangle?
3. Can the angles of any polygon sum to more than $360^\circ$?
4. Why do the angles around a point always sum to $360^\circ$?
5. How would the angle $k$ change if the triangle were isosceles?

Tip:

When solving problems involving polygons, always remember the relationship between the sum of interior angles and the number of sides! For an $n$-sided polygon, the sum of its interior angles is $180(n-2)$ degrees.