We need to find the size of angle $k$ in the given figure. The figure shows a triangle with an external angle of $244^\circ$. The other two angles adjacent to the external angle are $29^\circ$ and $35^\circ$.

1. Problem Description

We need to find the size of angle $k$ in the given figure. The figure shows a triangle with an external angle of $244^\circ$. The other two angles adjacent to the external angle are $29^\circ$ and $35^\circ$.

2. Solution Steps

First, we need to find the interior angles of the triangle at the vertices where the $29^\circ$ and $35^\circ$ angles are given. Let's call these angles $a$ and $b$ respectively.

Since the external angle is $244^\circ$, the interior angle adjacent to it is $360^\circ - 244^\circ = 116^\circ$.

The sum of angles around a point is $360^\circ$, so we can determine the interior angles $a$ and $b$.

$a = 180^\circ - 29^\circ = 151^\circ$ is incorrect.

The angles $29^\circ$ and $35^\circ$ are angles exterior to two other interior angles. Let the angles adjacent to $29^\circ$ and $35^\circ$ be $x$ and $y$. Then $x + y = 116^\circ$, where $116^\circ$ is the angle exterior to the $244^\circ$ angle. We also have the following equations:

$a = 180^\circ - 29^\circ$

$b = 180^\circ - 35^\circ$

We know that the sum of the angles $x, 29^\circ$ and $y, 35^\circ$ are on a straight line that form an external angle of $244^\circ$. Thus, the angle on that vertex can also be expressed as $360^\circ - 244^\circ = 116^\circ$.

So the three angles adjacent to the external angles $29^\circ$, $35^\circ$, and $244^\circ$ sum to $116^\circ$.

To find angle $k$, we need to find the remaining two angles of the large triangle.

The two given angles are:

$a = 180^\circ - 29^\circ - (360^\circ - 244^\circ) = 180^\circ - 29^\circ - 116^\circ = 35^\circ$

$b = 180^\circ - 35^\circ - (360^\circ - 244^\circ) = 180^\circ - 35^\circ - 116^\circ = 29^\circ$

So, we have interior angles of $29^\circ$ and $35^\circ$ at the bottom corners of the large triangle. Since the sum of angles in a triangle is $180^\circ$, we can write:

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

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

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

$k = 116^\circ$

3. Final Answer

116