Final answer:
Without additional information on the relationship between angles EDC, 27DC, and EDT, or a provided diagram, it's not possible to accurately determine m∠EDC, especially since none of the provided answer choices match the calculation of 180° - 81° = 99°.
Step-by-step explanation:
To find the measure of angle EDC, also denoted as m∠EDC, we need to understand the relationships between the given angles. We know that angle 27DC is 81° and angle EDT is 96°. If angle EDC and angle 27DC are supplementary angles (angles that add up to 180° when they are adjacent), their measures should add up to 180°. Similarly, if angle EDT and angle EDC are supplementary, their measures will also add up to 180°.
Since no diagram was provided, we must assume from the context that angle EDC is supplementary to both given angles based on standard notation for geometric figures. Hence, we can calculate m∠EDC by subtracting m∠27DC from 180°:
180° - 81° = 99°.
But because 99° is not one of the provided options, we should consider that angle EDT is also involved. Since none of the information provided directly answers the question, and since the given choices for m∠EDC do not include 99°, it appears that there might be a mistake or an assumption in the question that we are not aware of, such as missing information regarding the relationship between the angles. Thus, without additional information, we cannot accurately determine the measure of angle EDC.