We are given an isosceles triangle with one angle equal to $58^\circ$. The two other angles, $m$ and $n$, are equal in size. We want to find the size of angle $m$.

1. Problem Description

We are given an isosceles triangle with one angle equal to $58^\circ$. The two other angles, $m$ and $n$, are equal in size. We want to find the size of angle $m$.

2. Solution Steps

The sum of the angles in any triangle is $180^\circ$.

We know that one angle is $58^\circ$, and the other two angles, $m$ and $n$, are equal.

So we have:

$m + n + 58^\circ = 180^\circ$.

Since $m = n$, we can rewrite the equation as:

$m + m + 58^\circ = 180^\circ$.

$2m + 58^\circ = 180^\circ$.

Subtract $58^\circ$ from both sides:

$2m = 180^\circ - 58^\circ$.

$2m = 122^\circ$.

Divide both sides by 2:

$m = \frac{122^\circ}{2}$.

$m = 61^\circ$.

3. Final Answer

The size of angle $m$ is $61^\circ$.