1. The problem states that the measure of angle $\angle HIJ$ is given as 94°. 2. It also states that $m \angle HIJ = 90^\circ$, which is a contradiction because an angle cannot be both 94° and 90° at the same time. 3. To clarify, if $\angle HIJ$ is 94°, then it is an obtuse angle (greater than 90°). 4. If $m \angle HIJ = 90^\circ$, then it is a right angle. 5. Since the problem shows $\angle HIJ = 94^\circ$, the correct measure of the angle is 94°, not 90°. 6. Therefore, the measure of $\angle HIJ$ is $\boxed{94^\circ}$.