Question: Work out the size of angle $k$. Not drawn accurately. Zoom 83° k top-left: icon of a small calculator/checkmark near the top; center: geometry diagram with angle $k$ in a purple region at the bottom-right vertex and 83° in a green region adjacent to it, with matching tick marks on the left slanted side, the bottom side, and the diagonal side indicating an isosceles triangle; bottom-right: text "Not drawn accurately"
1. **State the problem:** We need to find the size of angle $k$ in a triangle where one angle is $83^\circ$ and the triangle is isosceles.
2. **Identify the properties:** In an isosceles triangle, two sides are equal, and the angles opposite those sides are equal.
3. **Label the triangle:** Let the triangle have angles $k$, $k$, and $83^\circ$ since the two equal sides imply two equal angles.
4. **Use the triangle angle sum rule:** The sum of interior angles in any triangle is $180^\circ$.
5. **Set up the equation:**
$$k + k + 83 = 180$$
6. **Simplify:**
$$2k + 83 = 180$$
7. **Isolate $k$:**
$$2k = 180 - 83$$
$$2k = 97$$
8. **Divide both sides by 2:**
$$\cancel{2}k = \frac{97}{\cancel{2}}$$
$$k = 48.5$$
9. **Conclusion:** The size of angle $k$ is $48.5^\circ$.