The sum of the interior angles of a triangle is always 180 degrees. If two angles each measure 34 degrees, you can find the third angle by using the following equation:
\[ \text{Third angle} = 180^\circ - (\text{First angle} + \text{Second angle}) \]
Substituting the known values:
\[ \text{Third angle} = 180^\circ - (34^\circ + 34^\circ) \] \[ \text{Third angle} = 180^\circ - 68^\circ \] \[ \text{Third angle} = 112^\circ \]
Therefore, the measurement of the third interior angle is 112 degrees.