Final answer:
The measure of angle ADE in rhombus ABCD is 59 degrees, calculated by subtracting the sum of the given angle ECD (31 degrees) and the right angle (90 degrees) from the total sum of angles in a triangle (180 degrees).
Step-by-step explanation:
The student's question asks for the measure of angle ADE in rhombus ABCD, provided the measure of angle ECD is 31 degrees. Since ABCD is a rhombus, the diagonals bisect each other at right angles, which implies that triangle ADE is a right-angled triangle.
Furthermore, diagonals of a rhombus are perpendicular bisectors, which means that angle AED is also 90 degrees. The sum of the interior angles in any triangle is always 180 degrees. Therefore, the measure of angle ADE can be found by subtracting the sum of angles ECD and AED from 180 degrees.
m angle ADE = 180 degrees - (m angle ECD + m angle AED)
m angle ADE = 180 degrees - (31 degrees + 90 degrees)
m angle ADE = 180 degrees - 121 degrees
m angle ADE = 59 degrees
The complete question is:In rhombus ABCD, m triangle ECD = 31. What is m triangle ADE? Enter your answer in the box. is: