The angle ABC is straight, the angle DEK is 20% of the angle ABC, and the value of the angle MON

The angle ABC is straight, the angle DEK is 20% of the angle ABC, and the value of the angle MON is equal to the average orithmetic of the angles ABC and DEK. Find the angles DEK and MON.

1. Since the angle ABC is straight, it is equal to 90 degrees. Let’s denote the angle DEK as x. Then:
90 degrees = 100%;
x = 20%.
Let’s find x by proportion:
x = 90 * 20/100 = 1800/100 = 18.
Angle DEK = x = 18 degrees.
2. The arithmetic mean is the sum of all numbers divided by the number of these numbers, that is:
angle MON = (angle ABC + angle DEK) / 2;
angle MON = (90 + 18) / 2 = 108/2 = 54 (degrees).
Answer: DEK angle = 18 degrees, MON angle = 54 degrees.