The CF beam divides the deployed angle MCN into two angles MCF and FCN.

The CF beam divides the deployed angle MCN into two angles MCF and FCN. Find the degree measure of these angles if the FCN angle is 3.5 times less than the MCF angle.

Since we do not know both angles, we introduce a variable. Let x be the smaller FCN angle, then the MCF angle will be 3.5x, since the FCN angle is 3.5 times less than the MCF angle.

The corners MCF and FCN are adjacent corners.

The sum of adjacent angles is 180 °. Let’s make the equation:

3.5x + x = 180.

4.5x = 180.

x = 180: 4.5.

x = 40.

This means that the FCN angle is 40 °.

The MCF angle can be found in two ways:

1) Angle MCF = 3.5x = 3.5 * 40 = 140 °.

2) Angle MCF = 180 ° – FCN = 180 ° – 40 ° = 140 °.

Answer: FCN angle is 40 °, MCF angle is 140 °.