Chapter P - Preliminary Concepts - P.3 - Informal Geometry and Measurement - Exercises P.3 - Page 24: 42

$$ 34 ^{\circ}$$

Since the measures of angle 1 and angle 2 are equal, and both angles add up to get the measure of angle ABC, it follows that these angles bisect angle ABC. By definition, the angles which bisect the larger angles are half the value of the larger angle. From this, it follows: $$ m \angle 1 = \frac{68^{\circ}}{2} \\ = 34^{\circ}$$