The CE beam divides the deployed angle MCK into two angles MCE and EK. Find the degree measure

The CE beam divides the deployed angle MCK into two angles MCE and EK. Find the degree measure of these angles if the ECK angle is 3.5 times less than the MCE angle.

Suppose that the ECK angle is x, then the MCE angle is 3.5x.

Since the degree measure of the extended angle MCК is equal to 180, then we compose and solve the equation

MCE angle + ECK angle = MСK angle, substitute the values

3.5x + x = 180,

4.5x = 180,

x = 180: 4.5,

x = 40.

This means that the ECK angle is 40.

Find the value of the angle MCE

3.5 * 400 = 140.

Answer: the ECK angle is 40, the MCE angle is 140.