We are given a triangle with one angle equal to $58^\circ$. One of the exterior angles is $103^\circ$. We need to find the size of angle $f$, which is an interior angle of the triangle.

1. Problem Description

We are given a triangle with one angle equal to $58^\circ$. One of the exterior angles is $103^\circ$. We need to find the size of angle $f$, which is an interior angle of the triangle.

2. Solution Steps

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Let the three interior angles of the triangle be $58^\circ$, $f$, and $x$. The exterior angle adjacent to $x$ is $103^\circ$.

Therefore, we have

$58^\circ + f = 103^\circ$

Subtracting $58^\circ$ from both sides, we get:

$f = 103^\circ - 58^\circ$

$f = 45^\circ$

3. Final Answer

The size of angle $f$ is $45^\circ$.