Answer:
Step-by-step explanation:To determine the measure of angle CDE (m∠CDE), we need to consider the given information and apply the appropriate geometric properties and relationships.
From the given information:
1. bc⊥ac implies that line segment AC and line segment BC are perpendicular to each other.
Using the properties of perpendicular lines and angles, we can determine the measure of angle CDE:
2. Since line segment BC is perpendicular to line segment AC, angle BAC and angle CDE are corresponding angles.
3. Corresponding angles that are formed by a transversal and two parallel lines are congruent.
4. Therefore, m∠BAC = m∠CDE.
Now, using the additional given information:
5. m∠BAC = 32°.
Thus, we can conclude:
6. m∠CDE = m∠BAC = 32°.
Therefore, the measure of angle CDE (m∠CDE) is 32°, based on the given information and the properties of perpendicular lines and corresponding angles.