We are given a figure that looks like a quadrilateral formed by a triangle and a rectangle. One angle of the quadrilateral is given as $150^\circ$. Two angles are right angles, $90^\circ$. The triangle is isosceles. We are asked to find the size of angle $k$, which is one of the angles in the isosceles triangle.

1. Problem Description

We are given a figure that looks like a quadrilateral formed by a triangle and a rectangle. One angle of the quadrilateral is given as $150^\circ$. Two angles are right angles, $90^\circ$. The triangle is isosceles. We are asked to find the size of angle $k$, which is one of the angles in the isosceles triangle.

2. Solution Steps

The sum of the interior angles of a quadrilateral is $360^\circ$. Let the unknown angle adjacent to the $150^\circ$ angle be $x$. We can write:

$90^\circ + 90^\circ + 150^\circ + x = 360^\circ$

$330^\circ + x = 360^\circ$

$x = 360^\circ - 330^\circ$

$x = 30^\circ$

Now, consider the triangle. Since the triangle is isosceles, the two angles opposite the equal sides are equal. Let the angles be $k$ and $k$.

Then, $k + k + x = 180^\circ$

$2k + 30^\circ = 180^\circ$

$2k = 180^\circ - 30^\circ$

$2k = 150^\circ$

$k = \frac{150^\circ}{2}$

$k = 75^\circ$

3. Final Answer

The size of angle $k$ is $75^\circ$.