The CE beam divides the right angle DCM into two angles DCE and ECM. Find the degree measure

The CE beam divides the right angle DCM into two angles DCE and ECM. Find the degree measure of these angles if the DCE angle is 2/5 of the DCM angle.

First of all, from the very beginning, we should note that the degree measure of the DCM angle is 90o, since this angle is, by condition, right.

Secondly, now we need to determine the degree measure of the DCE angle. According to the condition, its share in the total value of the DCM angle is equal to 2/5. So, to find the DCE angle, you need to multiply 90o by 2/5. Then we get:

DCE = 90 * 2/5 = 36o.

Now, given that DCE + ECM = 90o, determine the value of the ECM angle:

ECM = 90o – 36o = 54o.

Answer: DCE = 36o, ECM = 54o.