Final answer:
To finish a measure that starts with two eighth notes in a common 4/4 time signature, a quarter rest is needed to fill one full beat of silence. Another quarter rest would then be used to complete the remaining two beats of the measure.
Step-by-step explanation:
The question is asking to complete a measure in music notation with a rest that fills the remaining time for that measure. Given that there are two eighth notes at the beginning of the measure, and assuming that we're working within a common time signature like 4/4, these two eighth notes will occupy half a beat each, totaling one beat together.
The correct rest to complete the measure, which consists of four beats in a common time signature, would be a quarter rest. A quarter rest corresponds to one full beat of silence, thus using one would bring the total beats in the measure to two (the two eighth notes and the one quarter rest), leaving two more beats to complete the measure. Therefore, to finish the measure, we would need another quarter rest. Therefore, the correct answer is a quarter rest, not an eighth rest nor a sixteenth rest.