We are given a diagram with an angle $244^{\circ}$ around a point, and two other angles $29^{\circ}$ and $35^{\circ}$ also around that point. We need to find the angle $k$ in the triangle formed.

1. Problem Description

We are given a diagram with an angle $244^{\circ}$ around a point, and two other angles $29^{\circ}$ and $35^{\circ}$ also around that point. We need to find the angle $k$ in the triangle formed.

2. Solution Steps

First, we need to find the angle inside the triangle that is vertically opposite the $244^{\circ}$ angle. Let's call this angle $x$.

Since angles around a point sum to $360^{\circ}$, we have:

$x + 29^{\circ} + 35^{\circ} + 244^{\circ} = 360^{\circ}$

$x + 308^{\circ} = 360^{\circ}$

$x = 360^{\circ} - 308^{\circ}$

$x = 52^{\circ}$

Now we know the three internal angles at the central point add to $360^{\circ}$.

Let's consider the triangle. The angles of the triangle are $k$, $29^{\circ}$, and $35^{\circ}$. The sum of angles in a triangle is $180^{\circ}$. Thus, the angles around the point where the $244^{\circ}$ angle is defined also form a full rotation.

The internal angles are $29^{\circ}$ and $35^{\circ}$. Thus the other two angles that add up to $360^{\circ}$ are vertically opposite the interior angles of the triangle. The remaining angle must be $360 - 244 - 29 - 35 = 360 - 308 = 52$.

So we have two angles in the triangle which are $29^{\circ}$ and $35^{\circ}$. The sum of the angles in a triangle is $180^{\circ}$, therefore:

$k + 29^{\circ} + 35^{\circ} = 180^{\circ}$

$k + 64^{\circ} = 180^{\circ}$

$k = 180^{\circ} - 64^{\circ}$

$k = 116^{\circ}$

3. Final Answer

$k = 116^{\circ}$