Final answer:
In given scenario, the measure of angle ECB is 112 degrees. This is determined by considering the concepts of similar triangles, the properties of a right triangle, and the measures of the angles.
Step-by-step explanation:
The concept in question here is an application of geometry and angle measures, specifically in relation to triangles. Given that triangle ABC is a right triangle and point D is the midpoint of side AB, and point E is the midpoint of side AC, we have information about angle ADE, but we want to find the measure of angle ECB. We know that in a right triangle, the sum of the angles is 180 degrees. Since AD is half of AB and AE is half of AC, triangle ADE is similar to triangle ABC. Therefore, the angles at their corresponding vertices are equal. If angle ADE measures 68 degrees, angle ABC (or its supplement angle BCA) also measures 68 degrees. If ADB is a right angle (which it is, since ABC is given to be a right angle triangle), and knowing that the angles of a triangle sum to 180 degrees, angle DBA can be calculated as 180 - 90 - 68 = 22 degrees. Then, because DEB is a straight line, angle DBE is 180 - 22 = 158 degrees. Again, since triangle BEC is a right triangle, we can calculate angle EBC as 180 - 90 -158 = -68. The negative value implies that the real angle ECB measures its supplementary angle which is 180 + (-68) = 112 degrees.
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